[lmfit-py] 01/03: Imported Upstream version 0.9.3+dfsg
Frédéric-Emmanuel Picca
picca at moszumanska.debian.org
Thu Mar 31 17:06:56 UTC 2016
This is an automated email from the git hooks/post-receive script.
picca pushed a commit to branch master
in repository lmfit-py.
commit 7be530f22592e2d2193230d863b85d2f5c91c116
Author: Picca Frédéric-Emmanuel <picca at debian.org>
Date: Thu Mar 31 18:44:17 2016 +0200
Imported Upstream version 0.9.3+dfsg
---
INSTALL | 24 +-
LICENSE | 54 +-
MANIFEST.in | 24 +-
NIST_STRD/Bennett5.dat | 428 +--
NIST_STRD/BoxBOD.dat | 132 +-
NIST_STRD/Chwirut1.dat | 548 ++--
NIST_STRD/Chwirut2.dat | 228 +-
NIST_STRD/DanWood.dat | 132 +-
NIST_STRD/ENSO.dat | 456 ++--
NIST_STRD/Eckerle4.dat | 190 +-
NIST_STRD/Gauss1.dat | 620 ++---
NIST_STRD/Gauss2.dat | 620 ++---
NIST_STRD/Gauss3.dat | 620 ++---
NIST_STRD/Hahn1.dat | 592 ++--
NIST_STRD/Kirby2.dat | 422 +--
NIST_STRD/Lanczos1.dat | 168 +-
NIST_STRD/Lanczos2.dat | 168 +-
NIST_STRD/Lanczos3.dat | 168 +-
NIST_STRD/MGH09.dat | 142 +-
NIST_STRD/MGH10.dat | 152 +-
NIST_STRD/MGH17.dat | 186 +-
NIST_STRD/Misra1a.dat | 148 +-
NIST_STRD/Misra1b.dat | 148 +-
NIST_STRD/Misra1c.dat | 148 +-
NIST_STRD/Misra1d.dat | 148 +-
NIST_STRD/Nelson.dat | 376 +--
NIST_STRD/Rat42.dat | 138 +-
NIST_STRD/Rat43.dat | 150 +-
NIST_STRD/Roszman1.dat | 170 +-
NIST_STRD/Thurber.dat | 194 +-
PKG-INFO | 2 +-
README | 65 -
THANKS.txt | 48 +-
doc/Makefile | 224 +-
doc/__pycache__/extensions.cpython-35.pyc | Bin 0 -> 358 bytes
doc/_images/emcee_dbl_exp.png | Bin 0 -> 19442 bytes
doc/_images/emcee_dbl_exp2.png | Bin 0 -> 22518 bytes
doc/_images/emcee_triangle.png | Bin 0 -> 195958 bytes
doc/_templates/indexsidebar.html | 48 +-
doc/bounds.rst | 157 +-
doc/builtin_models.rst | 1923 ++++++-------
doc/conf.py | 363 +--
doc/confidence.rst | 370 +--
doc/constraints.rst | 332 +--
doc/contents.rst | 36 +-
doc/extensions.py | 20 +-
doc/extensions.pyc | Bin 406 -> 398 bytes
doc/faq.rst | 195 +-
doc/fitting.rst | 1519 ++++++-----
doc/index.rst | 136 +-
doc/installation.rst | 164 +-
doc/intro.rst | 300 +--
doc/model.rst | 2290 ++++++++--------
doc/parameters.rst | 477 ++--
doc/sphinx/ext_mathjax.py | 20 +-
doc/sphinx/ext_pngmath.py | 20 +-
doc/sphinx/theme/lmfitdoc/layout.html | 132 +-
doc/sphinx/theme/lmfitdoc/static/lmfitdoc.css_t | 696 ++---
doc/sphinx/theme/lmfitdoc/theme.conf | 8 +-
doc/support.rst | 60 +-
doc/whatsnew.rst | 194 +-
lmfit/__init__.py | 106 +-
lmfit/_differentialevolution.py | 1500 +++++------
lmfit/_version.py | 4 +-
lmfit/asteval.py | 1606 +++++------
lmfit/astutils.py | 516 ++--
lmfit/confidence.py | 835 +++---
lmfit/lineshapes.py | 572 ++--
lmfit/minimizer.py | 2056 ++++++++------
lmfit/model.py | 2098 ++++++++-------
lmfit/models.py | 938 +++----
lmfit/ordereddict.py | 256 +-
lmfit/parameter.py | 1543 ++++++-----
lmfit/printfuncs.py | 456 ++--
lmfit/ui/__init__.py | 96 +-
lmfit/ui/basefitter.py | 640 ++---
lmfit/ui/ipy_fitter.py | 564 ++--
lmfit/uncertainties/__init__.py | 3290 +++++++++++------------
lmfit/uncertainties/umath.py | 700 ++---
publish_docs.sh | 118 +-
requirements.txt | 4 +-
setup.py | 108 +-
tests/NISTModels.py | 396 +--
tests/_test_ci.py | 116 +-
tests/_test_make_paras_and_func.py | 62 +-
tests/lmfit_testutils.py | 36 +-
tests/test_1variable.py | 114 +-
tests/test_NIST_Strd.py | 534 ++--
tests/test_algebraic_constraint.py | 294 +-
tests/test_algebraic_constraint2.py | 206 +-
tests/test_basicfit.py | 94 +-
tests/test_bounded_jacobian.py | 86 +-
tests/test_bounds.py | 108 +-
tests/test_confidence.py | 132 +-
tests/test_copy_params.py | 72 +-
tests/test_default_kws.py | 48 +-
tests/test_itercb.py | 58 +-
tests/test_manypeaks_speed.py | 74 +-
tests/test_model.py | 1088 ++++----
tests/test_multidatasets.py | 148 +-
tests/test_nose.py | 1007 ++++---
tests/test_parameters.py | 259 +-
tests/test_params_set.py | 94 +-
tests/test_stepmodel.py | 116 +-
versioneer.py | 1802 ++++++-------
105 files changed, 21898 insertions(+), 20545 deletions(-)
diff --git a/INSTALL b/INSTALL
index 08c0ef0..712b012 100644
--- a/INSTALL
+++ b/INSTALL
@@ -1,12 +1,12 @@
-Installation instructions for LMFIT-py
-========================================
-
-To install the lmfit python module, use::
-
- python setup.py build
- python setup.py install
-
-Python 2.6 or higher is required, as are numpy and scipy.
-
-Matt Newville <newville at cars.uchicago.edu>
-Last Update: 2013-Dec-15
+Installation instructions for LMFIT-py
+========================================
+
+To install the lmfit python module, use::
+
+ python setup.py build
+ python setup.py install
+
+Python 2.6 or higher is required, as are numpy and scipy.
+
+Matt Newville <newville at cars.uchicago.edu>
+Last Update: 2013-Dec-15
diff --git a/LICENSE b/LICENSE
index 9b3aa46..174874e 100644
--- a/LICENSE
+++ b/LICENSE
@@ -1,27 +1,27 @@
-Copyright, Licensing, and Re-distribution
------------------------------------------
-
-The LMFIT-py code is distribution under the following license:
-
- Copyright (c) 2014 Matthew Newville, The University of Chicago
- Till Stensitzki, Freie Universitat Berlin
- Daniel B. Allen, Johns Hopkins University
- Michal Rawlik, Eidgenossische Technische Hochschule, Zurich
- Antonino Ingargiola, University of California, Los Angeles
- A. R. J. Nelson, Australian Nuclear Science and Technology Organisation
-
- Permission to use and redistribute the source code or binary forms of this
- software and its documentation, with or without modification is hereby
- granted provided that the above notice of copyright, these terms of use,
- and the disclaimer of warranty below appear in the source code and
- documentation, and that none of the names of above institutions or
- authors appear in advertising or endorsement of works derived from this
- software without specific prior written permission from all parties.
-
- THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
- IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
- FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
- THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
- LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
- FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
- DEALINGS IN THIS SOFTWARE.
+Copyright, Licensing, and Re-distribution
+-----------------------------------------
+
+The LMFIT-py code is distribution under the following license:
+
+ Copyright (c) 2014 Matthew Newville, The University of Chicago
+ Till Stensitzki, Freie Universitat Berlin
+ Daniel B. Allen, Johns Hopkins University
+ Michal Rawlik, Eidgenossische Technische Hochschule, Zurich
+ Antonino Ingargiola, University of California, Los Angeles
+ A. R. J. Nelson, Australian Nuclear Science and Technology Organisation
+
+ Permission to use and redistribute the source code or binary forms of this
+ software and its documentation, with or without modification is hereby
+ granted provided that the above notice of copyright, these terms of use,
+ and the disclaimer of warranty below appear in the source code and
+ documentation, and that none of the names of above institutions or
+ authors appear in advertising or endorsement of works derived from this
+ software without specific prior written permission from all parties.
+
+ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+ DEALINGS IN THIS SOFTWARE.
diff --git a/MANIFEST.in b/MANIFEST.in
index d83b8ba..1f48260 100644
--- a/MANIFEST.in
+++ b/MANIFEST.in
@@ -1,12 +1,12 @@
-include README.txt INSTALL LICENSE MANIFEST.in PKG-INFO THANKS.txt
-include setup.py publish_docs.sh
-include requirements.txt
-exclude *.pyc core.* *~ *.pdf
-recursive-include lmfit *.py
-recursive-include tests *.py *.dat
-recursive-include NIST_STRD *.dat
-recursive-include doc *
-recursive-exclude doc/_build *
-recursive-exclude doc *.pdf
-include versioneer.py
-include lmfit/_version.py
+include README.txt INSTALL LICENSE MANIFEST.in PKG-INFO THANKS.txt
+include setup.py publish_docs.sh
+include requirements.txt
+exclude *.pyc core.* *~ *.pdf
+recursive-include lmfit *.py
+recursive-include tests *.py *.dat
+recursive-include NIST_STRD *.dat
+recursive-include doc *
+recursive-exclude doc/_build *
+recursive-exclude doc *.pdf
+include versioneer.py
+include lmfit/_version.py
diff --git a/NIST_STRD/Bennett5.dat b/NIST_STRD/Bennett5.dat
index eba218a..51335f4 100644
--- a/NIST_STRD/Bennett5.dat
+++ b/NIST_STRD/Bennett5.dat
@@ -1,214 +1,214 @@
-NIST/ITL StRD
-Dataset Name: Bennett5 (Bennett5.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 214)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- superconductivity magnetization modeling. The
- response variable is magnetism, and the predictor
- variable is the log of time in minutes.
-
-Reference: Bennett, L., L. Swartzendruber, and H. Brown,
- NIST (1994).
- Superconductivity Magnetization Modeling.
-
-
-
-
-
-
-Data: 1 Response Variable (y = magnetism)
- 1 Predictor Variable (x = log[time])
- 154 Observations
- Higher Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 3 Parameters (b1 to b3)
-
- y = b1 * (b2+x)**(-1/b3) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = -2000 -1500 -2.5235058043E+03 2.9715175411E+02
- b2 = 50 45 4.6736564644E+01 1.2448871856E+00
- b3 = 0.8 0.85 9.3218483193E-01 2.0272299378E-02
-
-Residual Sum of Squares: 5.2404744073E-04
-Residual Standard Deviation: 1.8629312528E-03
-Degrees of Freedom: 151
-Number of Observations: 154
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- -34.834702E0 7.447168E0
- -34.393200E0 8.102586E0
- -34.152901E0 8.452547E0
- -33.979099E0 8.711278E0
- -33.845901E0 8.916774E0
- -33.732899E0 9.087155E0
- -33.640301E0 9.232590E0
- -33.559200E0 9.359535E0
- -33.486801E0 9.472166E0
- -33.423100E0 9.573384E0
- -33.365101E0 9.665293E0
- -33.313000E0 9.749461E0
- -33.260899E0 9.827092E0
- -33.217400E0 9.899128E0
- -33.176899E0 9.966321E0
- -33.139198E0 10.029280E0
- -33.101601E0 10.088510E0
- -33.066799E0 10.144430E0
- -33.035000E0 10.197380E0
- -33.003101E0 10.247670E0
- -32.971298E0 10.295560E0
- -32.942299E0 10.341250E0
- -32.916302E0 10.384950E0
- -32.890202E0 10.426820E0
- -32.864101E0 10.467000E0
- -32.841000E0 10.505640E0
- -32.817799E0 10.542830E0
- -32.797501E0 10.578690E0
- -32.774300E0 10.613310E0
- -32.757000E0 10.646780E0
- -32.733799E0 10.679150E0
- -32.716400E0 10.710520E0
- -32.699100E0 10.740920E0
- -32.678799E0 10.770440E0
- -32.661400E0 10.799100E0
- -32.644001E0 10.826970E0
- -32.626701E0 10.854080E0
- -32.612202E0 10.880470E0
- -32.597698E0 10.906190E0
- -32.583199E0 10.931260E0
- -32.568699E0 10.955720E0
- -32.554298E0 10.979590E0
- -32.539799E0 11.002910E0
- -32.525299E0 11.025700E0
- -32.510799E0 11.047980E0
- -32.499199E0 11.069770E0
- -32.487598E0 11.091100E0
- -32.473202E0 11.111980E0
- -32.461601E0 11.132440E0
- -32.435501E0 11.152480E0
- -32.435501E0 11.172130E0
- -32.426800E0 11.191410E0
- -32.412300E0 11.210310E0
- -32.400799E0 11.228870E0
- -32.392101E0 11.247090E0
- -32.380501E0 11.264980E0
- -32.366001E0 11.282560E0
- -32.357300E0 11.299840E0
- -32.348598E0 11.316820E0
- -32.339901E0 11.333520E0
- -32.328400E0 11.349940E0
- -32.319698E0 11.366100E0
- -32.311001E0 11.382000E0
- -32.299400E0 11.397660E0
- -32.290699E0 11.413070E0
- -32.282001E0 11.428240E0
- -32.273300E0 11.443200E0
- -32.264599E0 11.457930E0
- -32.256001E0 11.472440E0
- -32.247299E0 11.486750E0
- -32.238602E0 11.500860E0
- -32.229900E0 11.514770E0
- -32.224098E0 11.528490E0
- -32.215401E0 11.542020E0
- -32.203800E0 11.555380E0
- -32.198002E0 11.568550E0
- -32.189400E0 11.581560E0
- -32.183601E0 11.594420E0
- -32.174900E0 11.607121E0
- -32.169102E0 11.619640E0
- -32.163300E0 11.632000E0
- -32.154598E0 11.644210E0
- -32.145901E0 11.656280E0
- -32.140099E0 11.668200E0
- -32.131401E0 11.679980E0
- -32.125599E0 11.691620E0
- -32.119801E0 11.703130E0
- -32.111198E0 11.714510E0
- -32.105400E0 11.725760E0
- -32.096699E0 11.736880E0
- -32.090900E0 11.747890E0
- -32.088001E0 11.758780E0
- -32.079300E0 11.769550E0
- -32.073502E0 11.780200E0
- -32.067699E0 11.790730E0
- -32.061901E0 11.801160E0
- -32.056099E0 11.811480E0
- -32.050301E0 11.821700E0
- -32.044498E0 11.831810E0
- -32.038799E0 11.841820E0
- -32.033001E0 11.851730E0
- -32.027199E0 11.861550E0
- -32.024300E0 11.871270E0
- -32.018501E0 11.880890E0
- -32.012699E0 11.890420E0
- -32.004002E0 11.899870E0
- -32.001099E0 11.909220E0
- -31.995300E0 11.918490E0
- -31.989500E0 11.927680E0
- -31.983700E0 11.936780E0
- -31.977900E0 11.945790E0
- -31.972099E0 11.954730E0
- -31.969299E0 11.963590E0
- -31.963501E0 11.972370E0
- -31.957701E0 11.981070E0
- -31.951900E0 11.989700E0
- -31.946100E0 11.998260E0
- -31.940300E0 12.006740E0
- -31.937401E0 12.015150E0
- -31.931601E0 12.023490E0
- -31.925800E0 12.031760E0
- -31.922899E0 12.039970E0
- -31.917101E0 12.048100E0
- -31.911301E0 12.056170E0
- -31.908400E0 12.064180E0
- -31.902599E0 12.072120E0
- -31.896900E0 12.080010E0
- -31.893999E0 12.087820E0
- -31.888201E0 12.095580E0
- -31.885300E0 12.103280E0
- -31.882401E0 12.110920E0
- -31.876600E0 12.118500E0
- -31.873699E0 12.126030E0
- -31.867901E0 12.133500E0
- -31.862101E0 12.140910E0
- -31.859200E0 12.148270E0
- -31.856300E0 12.155570E0
- -31.850500E0 12.162830E0
- -31.844700E0 12.170030E0
- -31.841801E0 12.177170E0
- -31.838900E0 12.184270E0
- -31.833099E0 12.191320E0
- -31.830200E0 12.198320E0
- -31.827299E0 12.205270E0
- -31.821600E0 12.212170E0
- -31.818701E0 12.219030E0
- -31.812901E0 12.225840E0
- -31.809999E0 12.232600E0
- -31.807100E0 12.239320E0
- -31.801300E0 12.245990E0
- -31.798401E0 12.252620E0
- -31.795500E0 12.259200E0
- -31.789700E0 12.265750E0
- -31.786800E0 12.272240E0
+NIST/ITL StRD
+Dataset Name: Bennett5 (Bennett5.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 43)
+ Certified Values (lines 41 to 48)
+ Data (lines 61 to 214)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are the result of a NIST study involving
+ superconductivity magnetization modeling. The
+ response variable is magnetism, and the predictor
+ variable is the log of time in minutes.
+
+Reference: Bennett, L., L. Swartzendruber, and H. Brown,
+ NIST (1994).
+ Superconductivity Magnetization Modeling.
+
+
+
+
+
+
+Data: 1 Response Variable (y = magnetism)
+ 1 Predictor Variable (x = log[time])
+ 154 Observations
+ Higher Level of Difficulty
+ Observed Data
+
+Model: Miscellaneous Class
+ 3 Parameters (b1 to b3)
+
+ y = b1 * (b2+x)**(-1/b3) + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = -2000 -1500 -2.5235058043E+03 2.9715175411E+02
+ b2 = 50 45 4.6736564644E+01 1.2448871856E+00
+ b3 = 0.8 0.85 9.3218483193E-01 2.0272299378E-02
+
+Residual Sum of Squares: 5.2404744073E-04
+Residual Standard Deviation: 1.8629312528E-03
+Degrees of Freedom: 151
+Number of Observations: 154
+
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ -34.834702E0 7.447168E0
+ -34.393200E0 8.102586E0
+ -34.152901E0 8.452547E0
+ -33.979099E0 8.711278E0
+ -33.845901E0 8.916774E0
+ -33.732899E0 9.087155E0
+ -33.640301E0 9.232590E0
+ -33.559200E0 9.359535E0
+ -33.486801E0 9.472166E0
+ -33.423100E0 9.573384E0
+ -33.365101E0 9.665293E0
+ -33.313000E0 9.749461E0
+ -33.260899E0 9.827092E0
+ -33.217400E0 9.899128E0
+ -33.176899E0 9.966321E0
+ -33.139198E0 10.029280E0
+ -33.101601E0 10.088510E0
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+ -32.426800E0 11.191410E0
+ -32.412300E0 11.210310E0
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+ -32.392101E0 11.247090E0
+ -32.380501E0 11.264980E0
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+ -32.273300E0 11.443200E0
+ -32.264599E0 11.457930E0
+ -32.256001E0 11.472440E0
+ -32.247299E0 11.486750E0
+ -32.238602E0 11.500860E0
+ -32.229900E0 11.514770E0
+ -32.224098E0 11.528490E0
+ -32.215401E0 11.542020E0
+ -32.203800E0 11.555380E0
+ -32.198002E0 11.568550E0
+ -32.189400E0 11.581560E0
+ -32.183601E0 11.594420E0
+ -32.174900E0 11.607121E0
+ -32.169102E0 11.619640E0
+ -32.163300E0 11.632000E0
+ -32.154598E0 11.644210E0
+ -32.145901E0 11.656280E0
+ -32.140099E0 11.668200E0
+ -32.131401E0 11.679980E0
+ -32.125599E0 11.691620E0
+ -32.119801E0 11.703130E0
+ -32.111198E0 11.714510E0
+ -32.105400E0 11.725760E0
+ -32.096699E0 11.736880E0
+ -32.090900E0 11.747890E0
+ -32.088001E0 11.758780E0
+ -32.079300E0 11.769550E0
+ -32.073502E0 11.780200E0
+ -32.067699E0 11.790730E0
+ -32.061901E0 11.801160E0
+ -32.056099E0 11.811480E0
+ -32.050301E0 11.821700E0
+ -32.044498E0 11.831810E0
+ -32.038799E0 11.841820E0
+ -32.033001E0 11.851730E0
+ -32.027199E0 11.861550E0
+ -32.024300E0 11.871270E0
+ -32.018501E0 11.880890E0
+ -32.012699E0 11.890420E0
+ -32.004002E0 11.899870E0
+ -32.001099E0 11.909220E0
+ -31.995300E0 11.918490E0
+ -31.989500E0 11.927680E0
+ -31.983700E0 11.936780E0
+ -31.977900E0 11.945790E0
+ -31.972099E0 11.954730E0
+ -31.969299E0 11.963590E0
+ -31.963501E0 11.972370E0
+ -31.957701E0 11.981070E0
+ -31.951900E0 11.989700E0
+ -31.946100E0 11.998260E0
+ -31.940300E0 12.006740E0
+ -31.937401E0 12.015150E0
+ -31.931601E0 12.023490E0
+ -31.925800E0 12.031760E0
+ -31.922899E0 12.039970E0
+ -31.917101E0 12.048100E0
+ -31.911301E0 12.056170E0
+ -31.908400E0 12.064180E0
+ -31.902599E0 12.072120E0
+ -31.896900E0 12.080010E0
+ -31.893999E0 12.087820E0
+ -31.888201E0 12.095580E0
+ -31.885300E0 12.103280E0
+ -31.882401E0 12.110920E0
+ -31.876600E0 12.118500E0
+ -31.873699E0 12.126030E0
+ -31.867901E0 12.133500E0
+ -31.862101E0 12.140910E0
+ -31.859200E0 12.148270E0
+ -31.856300E0 12.155570E0
+ -31.850500E0 12.162830E0
+ -31.844700E0 12.170030E0
+ -31.841801E0 12.177170E0
+ -31.838900E0 12.184270E0
+ -31.833099E0 12.191320E0
+ -31.830200E0 12.198320E0
+ -31.827299E0 12.205270E0
+ -31.821600E0 12.212170E0
+ -31.818701E0 12.219030E0
+ -31.812901E0 12.225840E0
+ -31.809999E0 12.232600E0
+ -31.807100E0 12.239320E0
+ -31.801300E0 12.245990E0
+ -31.798401E0 12.252620E0
+ -31.795500E0 12.259200E0
+ -31.789700E0 12.265750E0
+ -31.786800E0 12.272240E0
diff --git a/NIST_STRD/BoxBOD.dat b/NIST_STRD/BoxBOD.dat
index 6a742fd..49163c7 100644
--- a/NIST_STRD/BoxBOD.dat
+++ b/NIST_STRD/BoxBOD.dat
@@ -1,66 +1,66 @@
-NIST/ITL StRD
-Dataset Name: BoxBOD (BoxBOD.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 42)
- Certified Values (lines 41 to 47)
- Data (lines 61 to 66)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are described in detail in Box, Hunter and
- Hunter (1978). The response variable is biochemical
- oxygen demand (BOD) in mg/l, and the predictor
- variable is incubation time in days.
-
-
-Reference: Box, G. P., W. G. Hunter, and J. S. Hunter (1978).
- Statistics for Experimenters.
- New York, NY: Wiley, pp. 483-487.
-
-
-
-
-
-Data: 1 Response (y = biochemical oxygen demand)
- 1 Predictor (x = incubation time)
- 6 Observations
- Higher Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 2 Parameters (b1 and b2)
-
- y = b1*(1-exp[-b2*x]) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1 100 2.1380940889E+02 1.2354515176E+01
- b2 = 1 0.75 5.4723748542E-01 1.0455993237E-01
-
-Residual Sum of Squares: 1.1680088766E+03
-Residual Standard Deviation: 1.7088072423E+01
-Degrees of Freedom: 4
-Number of Observations: 6
-
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 109 1
- 149 2
- 149 3
- 191 5
- 213 7
- 224 10
+NIST/ITL StRD
+Dataset Name: BoxBOD (BoxBOD.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 42)
+ Certified Values (lines 41 to 47)
+ Data (lines 61 to 66)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are described in detail in Box, Hunter and
+ Hunter (1978). The response variable is biochemical
+ oxygen demand (BOD) in mg/l, and the predictor
+ variable is incubation time in days.
+
+
+Reference: Box, G. P., W. G. Hunter, and J. S. Hunter (1978).
+ Statistics for Experimenters.
+ New York, NY: Wiley, pp. 483-487.
+
+
+
+
+
+Data: 1 Response (y = biochemical oxygen demand)
+ 1 Predictor (x = incubation time)
+ 6 Observations
+ Higher Level of Difficulty
+ Observed Data
+
+Model: Exponential Class
+ 2 Parameters (b1 and b2)
+
+ y = b1*(1-exp[-b2*x]) + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 1 100 2.1380940889E+02 1.2354515176E+01
+ b2 = 1 0.75 5.4723748542E-01 1.0455993237E-01
+
+Residual Sum of Squares: 1.1680088766E+03
+Residual Standard Deviation: 1.7088072423E+01
+Degrees of Freedom: 4
+Number of Observations: 6
+
+
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 109 1
+ 149 2
+ 149 3
+ 191 5
+ 213 7
+ 224 10
diff --git a/NIST_STRD/Chwirut1.dat b/NIST_STRD/Chwirut1.dat
index 4ad8aa5..5e72e4e 100644
--- a/NIST_STRD/Chwirut1.dat
+++ b/NIST_STRD/Chwirut1.dat
@@ -1,274 +1,274 @@
-NIST/ITL StRD
-Dataset Name: Chwirut1 (Chwirut1.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 274)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- ultrasonic calibration. The response variable is
- ultrasonic response, and the predictor variable is
- metal distance.
-
-Reference: Chwirut, D., NIST (197?).
- Ultrasonic Reference Block Study.
-
-
-
-
-
-
-
-Data: 1 Response Variable (y = ultrasonic response)
- 1 Predictor Variable (x = metal distance)
- 214 Observations
- Lower Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 3 Parameters (b1 to b3)
-
- y = exp[-b1*x]/(b2+b3*x) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 0.1 0.15 1.9027818370E-01 2.1938557035E-02
- b2 = 0.01 0.008 6.1314004477E-03 3.4500025051E-04
- b3 = 0.02 0.010 1.0530908399E-02 7.9281847748E-04
-
-Residual Sum of Squares: 2.3844771393E+03
-Residual Standard Deviation: 3.3616721320E+00
-Degrees of Freedom: 211
-Number of Observations: 214
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 92.9000E0 0.5000E0
- 78.7000E0 0.6250E0
- 64.2000E0 0.7500E0
- 64.9000E0 0.8750E0
- 57.1000E0 1.0000E0
- 43.3000E0 1.2500E0
- 31.1000E0 1.7500E0
- 23.6000E0 2.2500E0
- 31.0500E0 1.7500E0
- 23.7750E0 2.2500E0
- 17.7375E0 2.7500E0
- 13.8000E0 3.2500E0
- 11.5875E0 3.7500E0
- 9.4125E0 4.2500E0
- 7.7250E0 4.7500E0
- 7.3500E0 5.2500E0
- 8.0250E0 5.7500E0
- 90.6000E0 0.5000E0
- 76.9000E0 0.6250E0
- 71.6000E0 0.7500E0
- 63.6000E0 0.8750E0
- 54.0000E0 1.0000E0
- 39.2000E0 1.2500E0
- 29.3000E0 1.7500E0
- 21.4000E0 2.2500E0
- 29.1750E0 1.7500E0
- 22.1250E0 2.2500E0
- 17.5125E0 2.7500E0
- 14.2500E0 3.2500E0
- 9.4500E0 3.7500E0
- 9.1500E0 4.2500E0
- 7.9125E0 4.7500E0
- 8.4750E0 5.2500E0
- 6.1125E0 5.7500E0
- 80.0000E0 0.5000E0
- 79.0000E0 0.6250E0
- 63.8000E0 0.7500E0
- 57.2000E0 0.8750E0
- 53.2000E0 1.0000E0
- 42.5000E0 1.2500E0
- 26.8000E0 1.7500E0
- 20.4000E0 2.2500E0
- 26.8500E0 1.7500E0
- 21.0000E0 2.2500E0
- 16.4625E0 2.7500E0
- 12.5250E0 3.2500E0
- 10.5375E0 3.7500E0
- 8.5875E0 4.2500E0
- 7.1250E0 4.7500E0
- 6.1125E0 5.2500E0
- 5.9625E0 5.7500E0
- 74.1000E0 0.5000E0
- 67.3000E0 0.6250E0
- 60.8000E0 0.7500E0
- 55.5000E0 0.8750E0
- 50.3000E0 1.0000E0
- 41.0000E0 1.2500E0
- 29.4000E0 1.7500E0
- 20.4000E0 2.2500E0
- 29.3625E0 1.7500E0
- 21.1500E0 2.2500E0
- 16.7625E0 2.7500E0
- 13.2000E0 3.2500E0
- 10.8750E0 3.7500E0
- 8.1750E0 4.2500E0
- 7.3500E0 4.7500E0
- 5.9625E0 5.2500E0
- 5.6250E0 5.7500E0
- 81.5000E0 .5000E0
- 62.4000E0 .7500E0
- 32.5000E0 1.5000E0
- 12.4100E0 3.0000E0
- 13.1200E0 3.0000E0
- 15.5600E0 3.0000E0
- 5.6300E0 6.0000E0
- 78.0000E0 .5000E0
- 59.9000E0 .7500E0
- 33.2000E0 1.5000E0
- 13.8400E0 3.0000E0
- 12.7500E0 3.0000E0
- 14.6200E0 3.0000E0
- 3.9400E0 6.0000E0
- 76.8000E0 .5000E0
- 61.0000E0 .7500E0
- 32.9000E0 1.5000E0
- 13.8700E0 3.0000E0
- 11.8100E0 3.0000E0
- 13.3100E0 3.0000E0
- 5.4400E0 6.0000E0
- 78.0000E0 .5000E0
- 63.5000E0 .7500E0
- 33.8000E0 1.5000E0
- 12.5600E0 3.0000E0
- 5.6300E0 6.0000E0
- 12.7500E0 3.0000E0
- 13.1200E0 3.0000E0
- 5.4400E0 6.0000E0
- 76.8000E0 .5000E0
- 60.0000E0 .7500E0
- 47.8000E0 1.0000E0
- 32.0000E0 1.5000E0
- 22.2000E0 2.0000E0
- 22.5700E0 2.0000E0
- 18.8200E0 2.5000E0
- 13.9500E0 3.0000E0
- 11.2500E0 4.0000E0
- 9.0000E0 5.0000E0
- 6.6700E0 6.0000E0
- 75.8000E0 .5000E0
- 62.0000E0 .7500E0
- 48.8000E0 1.0000E0
- 35.2000E0 1.5000E0
- 20.0000E0 2.0000E0
- 20.3200E0 2.0000E0
- 19.3100E0 2.5000E0
- 12.7500E0 3.0000E0
- 10.4200E0 4.0000E0
- 7.3100E0 5.0000E0
- 7.4200E0 6.0000E0
- 70.5000E0 .5000E0
- 59.5000E0 .7500E0
- 48.5000E0 1.0000E0
- 35.8000E0 1.5000E0
- 21.0000E0 2.0000E0
- 21.6700E0 2.0000E0
- 21.0000E0 2.5000E0
- 15.6400E0 3.0000E0
- 8.1700E0 4.0000E0
- 8.5500E0 5.0000E0
- 10.1200E0 6.0000E0
- 78.0000E0 .5000E0
- 66.0000E0 .6250E0
- 62.0000E0 .7500E0
- 58.0000E0 .8750E0
- 47.7000E0 1.0000E0
- 37.8000E0 1.2500E0
- 20.2000E0 2.2500E0
- 21.0700E0 2.2500E0
- 13.8700E0 2.7500E0
- 9.6700E0 3.2500E0
- 7.7600E0 3.7500E0
- 5.4400E0 4.2500E0
- 4.8700E0 4.7500E0
- 4.0100E0 5.2500E0
- 3.7500E0 5.7500E0
- 24.1900E0 3.0000E0
- 25.7600E0 3.0000E0
- 18.0700E0 3.0000E0
- 11.8100E0 3.0000E0
- 12.0700E0 3.0000E0
- 16.1200E0 3.0000E0
- 70.8000E0 .5000E0
- 54.7000E0 .7500E0
- 48.0000E0 1.0000E0
- 39.8000E0 1.5000E0
- 29.8000E0 2.0000E0
- 23.7000E0 2.5000E0
- 29.6200E0 2.0000E0
- 23.8100E0 2.5000E0
- 17.7000E0 3.0000E0
- 11.5500E0 4.0000E0
- 12.0700E0 5.0000E0
- 8.7400E0 6.0000E0
- 80.7000E0 .5000E0
- 61.3000E0 .7500E0
- 47.5000E0 1.0000E0
- 29.0000E0 1.5000E0
- 24.0000E0 2.0000E0
- 17.7000E0 2.5000E0
- 24.5600E0 2.0000E0
- 18.6700E0 2.5000E0
- 16.2400E0 3.0000E0
- 8.7400E0 4.0000E0
- 7.8700E0 5.0000E0
- 8.5100E0 6.0000E0
- 66.7000E0 .5000E0
- 59.2000E0 .7500E0
- 40.8000E0 1.0000E0
- 30.7000E0 1.5000E0
- 25.7000E0 2.0000E0
- 16.3000E0 2.5000E0
- 25.9900E0 2.0000E0
- 16.9500E0 2.5000E0
- 13.3500E0 3.0000E0
- 8.6200E0 4.0000E0
- 7.2000E0 5.0000E0
- 6.6400E0 6.0000E0
- 13.6900E0 3.0000E0
- 81.0000E0 .5000E0
- 64.5000E0 .7500E0
- 35.5000E0 1.5000E0
- 13.3100E0 3.0000E0
- 4.8700E0 6.0000E0
- 12.9400E0 3.0000E0
- 5.0600E0 6.0000E0
- 15.1900E0 3.0000E0
- 14.6200E0 3.0000E0
- 15.6400E0 3.0000E0
- 25.5000E0 1.7500E0
- 25.9500E0 1.7500E0
- 81.7000E0 .5000E0
- 61.6000E0 .7500E0
- 29.8000E0 1.7500E0
- 29.8100E0 1.7500E0
- 17.1700E0 2.7500E0
- 10.3900E0 3.7500E0
- 28.4000E0 1.7500E0
- 28.6900E0 1.7500E0
- 81.3000E0 .5000E0
- 60.9000E0 .7500E0
- 16.6500E0 2.7500E0
- 10.0500E0 3.7500E0
- 28.9000E0 1.7500E0
- 28.9500E0 1.7500E0
+NIST/ITL StRD
+Dataset Name: Chwirut1 (Chwirut1.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 43)
+ Certified Values (lines 41 to 48)
+ Data (lines 61 to 274)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are the result of a NIST study involving
+ ultrasonic calibration. The response variable is
+ ultrasonic response, and the predictor variable is
+ metal distance.
+
+Reference: Chwirut, D., NIST (197?).
+ Ultrasonic Reference Block Study.
+
+
+
+
+
+
+
+Data: 1 Response Variable (y = ultrasonic response)
+ 1 Predictor Variable (x = metal distance)
+ 214 Observations
+ Lower Level of Difficulty
+ Observed Data
+
+Model: Exponential Class
+ 3 Parameters (b1 to b3)
+
+ y = exp[-b1*x]/(b2+b3*x) + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 0.1 0.15 1.9027818370E-01 2.1938557035E-02
+ b2 = 0.01 0.008 6.1314004477E-03 3.4500025051E-04
+ b3 = 0.02 0.010 1.0530908399E-02 7.9281847748E-04
+
+Residual Sum of Squares: 2.3844771393E+03
+Residual Standard Deviation: 3.3616721320E+00
+Degrees of Freedom: 211
+Number of Observations: 214
+
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 92.9000E0 0.5000E0
+ 78.7000E0 0.6250E0
+ 64.2000E0 0.7500E0
+ 64.9000E0 0.8750E0
+ 57.1000E0 1.0000E0
+ 43.3000E0 1.2500E0
+ 31.1000E0 1.7500E0
+ 23.6000E0 2.2500E0
+ 31.0500E0 1.7500E0
+ 23.7750E0 2.2500E0
+ 17.7375E0 2.7500E0
+ 13.8000E0 3.2500E0
+ 11.5875E0 3.7500E0
+ 9.4125E0 4.2500E0
+ 7.7250E0 4.7500E0
+ 7.3500E0 5.2500E0
+ 8.0250E0 5.7500E0
+ 90.6000E0 0.5000E0
+ 76.9000E0 0.6250E0
+ 71.6000E0 0.7500E0
+ 63.6000E0 0.8750E0
+ 54.0000E0 1.0000E0
+ 39.2000E0 1.2500E0
+ 29.3000E0 1.7500E0
+ 21.4000E0 2.2500E0
+ 29.1750E0 1.7500E0
+ 22.1250E0 2.2500E0
+ 17.5125E0 2.7500E0
+ 14.2500E0 3.2500E0
+ 9.4500E0 3.7500E0
+ 9.1500E0 4.2500E0
+ 7.9125E0 4.7500E0
+ 8.4750E0 5.2500E0
+ 6.1125E0 5.7500E0
+ 80.0000E0 0.5000E0
+ 79.0000E0 0.6250E0
+ 63.8000E0 0.7500E0
+ 57.2000E0 0.8750E0
+ 53.2000E0 1.0000E0
+ 42.5000E0 1.2500E0
+ 26.8000E0 1.7500E0
+ 20.4000E0 2.2500E0
+ 26.8500E0 1.7500E0
+ 21.0000E0 2.2500E0
+ 16.4625E0 2.7500E0
+ 12.5250E0 3.2500E0
+ 10.5375E0 3.7500E0
+ 8.5875E0 4.2500E0
+ 7.1250E0 4.7500E0
+ 6.1125E0 5.2500E0
+ 5.9625E0 5.7500E0
+ 74.1000E0 0.5000E0
+ 67.3000E0 0.6250E0
+ 60.8000E0 0.7500E0
+ 55.5000E0 0.8750E0
+ 50.3000E0 1.0000E0
+ 41.0000E0 1.2500E0
+ 29.4000E0 1.7500E0
+ 20.4000E0 2.2500E0
+ 29.3625E0 1.7500E0
+ 21.1500E0 2.2500E0
+ 16.7625E0 2.7500E0
+ 13.2000E0 3.2500E0
+ 10.8750E0 3.7500E0
+ 8.1750E0 4.2500E0
+ 7.3500E0 4.7500E0
+ 5.9625E0 5.2500E0
+ 5.6250E0 5.7500E0
+ 81.5000E0 .5000E0
+ 62.4000E0 .7500E0
+ 32.5000E0 1.5000E0
+ 12.4100E0 3.0000E0
+ 13.1200E0 3.0000E0
+ 15.5600E0 3.0000E0
+ 5.6300E0 6.0000E0
+ 78.0000E0 .5000E0
+ 59.9000E0 .7500E0
+ 33.2000E0 1.5000E0
+ 13.8400E0 3.0000E0
+ 12.7500E0 3.0000E0
+ 14.6200E0 3.0000E0
+ 3.9400E0 6.0000E0
+ 76.8000E0 .5000E0
+ 61.0000E0 .7500E0
+ 32.9000E0 1.5000E0
+ 13.8700E0 3.0000E0
+ 11.8100E0 3.0000E0
+ 13.3100E0 3.0000E0
+ 5.4400E0 6.0000E0
+ 78.0000E0 .5000E0
+ 63.5000E0 .7500E0
+ 33.8000E0 1.5000E0
+ 12.5600E0 3.0000E0
+ 5.6300E0 6.0000E0
+ 12.7500E0 3.0000E0
+ 13.1200E0 3.0000E0
+ 5.4400E0 6.0000E0
+ 76.8000E0 .5000E0
+ 60.0000E0 .7500E0
+ 47.8000E0 1.0000E0
+ 32.0000E0 1.5000E0
+ 22.2000E0 2.0000E0
+ 22.5700E0 2.0000E0
+ 18.8200E0 2.5000E0
+ 13.9500E0 3.0000E0
+ 11.2500E0 4.0000E0
+ 9.0000E0 5.0000E0
+ 6.6700E0 6.0000E0
+ 75.8000E0 .5000E0
+ 62.0000E0 .7500E0
+ 48.8000E0 1.0000E0
+ 35.2000E0 1.5000E0
+ 20.0000E0 2.0000E0
+ 20.3200E0 2.0000E0
+ 19.3100E0 2.5000E0
+ 12.7500E0 3.0000E0
+ 10.4200E0 4.0000E0
+ 7.3100E0 5.0000E0
+ 7.4200E0 6.0000E0
+ 70.5000E0 .5000E0
+ 59.5000E0 .7500E0
+ 48.5000E0 1.0000E0
+ 35.8000E0 1.5000E0
+ 21.0000E0 2.0000E0
+ 21.6700E0 2.0000E0
+ 21.0000E0 2.5000E0
+ 15.6400E0 3.0000E0
+ 8.1700E0 4.0000E0
+ 8.5500E0 5.0000E0
+ 10.1200E0 6.0000E0
+ 78.0000E0 .5000E0
+ 66.0000E0 .6250E0
+ 62.0000E0 .7500E0
+ 58.0000E0 .8750E0
+ 47.7000E0 1.0000E0
+ 37.8000E0 1.2500E0
+ 20.2000E0 2.2500E0
+ 21.0700E0 2.2500E0
+ 13.8700E0 2.7500E0
+ 9.6700E0 3.2500E0
+ 7.7600E0 3.7500E0
+ 5.4400E0 4.2500E0
+ 4.8700E0 4.7500E0
+ 4.0100E0 5.2500E0
+ 3.7500E0 5.7500E0
+ 24.1900E0 3.0000E0
+ 25.7600E0 3.0000E0
+ 18.0700E0 3.0000E0
+ 11.8100E0 3.0000E0
+ 12.0700E0 3.0000E0
+ 16.1200E0 3.0000E0
+ 70.8000E0 .5000E0
+ 54.7000E0 .7500E0
+ 48.0000E0 1.0000E0
+ 39.8000E0 1.5000E0
+ 29.8000E0 2.0000E0
+ 23.7000E0 2.5000E0
+ 29.6200E0 2.0000E0
+ 23.8100E0 2.5000E0
+ 17.7000E0 3.0000E0
+ 11.5500E0 4.0000E0
+ 12.0700E0 5.0000E0
+ 8.7400E0 6.0000E0
+ 80.7000E0 .5000E0
+ 61.3000E0 .7500E0
+ 47.5000E0 1.0000E0
+ 29.0000E0 1.5000E0
+ 24.0000E0 2.0000E0
+ 17.7000E0 2.5000E0
+ 24.5600E0 2.0000E0
+ 18.6700E0 2.5000E0
+ 16.2400E0 3.0000E0
+ 8.7400E0 4.0000E0
+ 7.8700E0 5.0000E0
+ 8.5100E0 6.0000E0
+ 66.7000E0 .5000E0
+ 59.2000E0 .7500E0
+ 40.8000E0 1.0000E0
+ 30.7000E0 1.5000E0
+ 25.7000E0 2.0000E0
+ 16.3000E0 2.5000E0
+ 25.9900E0 2.0000E0
+ 16.9500E0 2.5000E0
+ 13.3500E0 3.0000E0
+ 8.6200E0 4.0000E0
+ 7.2000E0 5.0000E0
+ 6.6400E0 6.0000E0
+ 13.6900E0 3.0000E0
+ 81.0000E0 .5000E0
+ 64.5000E0 .7500E0
+ 35.5000E0 1.5000E0
+ 13.3100E0 3.0000E0
+ 4.8700E0 6.0000E0
+ 12.9400E0 3.0000E0
+ 5.0600E0 6.0000E0
+ 15.1900E0 3.0000E0
+ 14.6200E0 3.0000E0
+ 15.6400E0 3.0000E0
+ 25.5000E0 1.7500E0
+ 25.9500E0 1.7500E0
+ 81.7000E0 .5000E0
+ 61.6000E0 .7500E0
+ 29.8000E0 1.7500E0
+ 29.8100E0 1.7500E0
+ 17.1700E0 2.7500E0
+ 10.3900E0 3.7500E0
+ 28.4000E0 1.7500E0
+ 28.6900E0 1.7500E0
+ 81.3000E0 .5000E0
+ 60.9000E0 .7500E0
+ 16.6500E0 2.7500E0
+ 10.0500E0 3.7500E0
+ 28.9000E0 1.7500E0
+ 28.9500E0 1.7500E0
diff --git a/NIST_STRD/Chwirut2.dat b/NIST_STRD/Chwirut2.dat
index 03703de..0651faa 100644
--- a/NIST_STRD/Chwirut2.dat
+++ b/NIST_STRD/Chwirut2.dat
@@ -1,114 +1,114 @@
-NIST/ITL StRD
-Dataset Name: Chwirut2 (Chwirut2.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 114)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- ultrasonic calibration. The response variable is
- ultrasonic response, and the predictor variable is
- metal distance.
-
-
-
-Reference: Chwirut, D., NIST (197?).
- Ultrasonic Reference Block Study.
-
-
-
-
-
-Data: 1 Response (y = ultrasonic response)
- 1 Predictor (x = metal distance)
- 54 Observations
- Lower Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 3 Parameters (b1 to b3)
-
- y = exp(-b1*x)/(b2+b3*x) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 0.1 0.15 1.6657666537E-01 3.8303286810E-02
- b2 = 0.01 0.008 5.1653291286E-03 6.6621605126E-04
- b3 = 0.02 0.010 1.2150007096E-02 1.5304234767E-03
-
-Residual Sum of Squares: 5.1304802941E+02
-Residual Standard Deviation: 3.1717133040E+00
-Degrees of Freedom: 51
-Number of Observations: 54
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 92.9000E0 0.500E0
- 57.1000E0 1.000E0
- 31.0500E0 1.750E0
- 11.5875E0 3.750E0
- 8.0250E0 5.750E0
- 63.6000E0 0.875E0
- 21.4000E0 2.250E0
- 14.2500E0 3.250E0
- 8.4750E0 5.250E0
- 63.8000E0 0.750E0
- 26.8000E0 1.750E0
- 16.4625E0 2.750E0
- 7.1250E0 4.750E0
- 67.3000E0 0.625E0
- 41.0000E0 1.250E0
- 21.1500E0 2.250E0
- 8.1750E0 4.250E0
- 81.5000E0 .500E0
- 13.1200E0 3.000E0
- 59.9000E0 .750E0
- 14.6200E0 3.000E0
- 32.9000E0 1.500E0
- 5.4400E0 6.000E0
- 12.5600E0 3.000E0
- 5.4400E0 6.000E0
- 32.0000E0 1.500E0
- 13.9500E0 3.000E0
- 75.8000E0 .500E0
- 20.0000E0 2.000E0
- 10.4200E0 4.000E0
- 59.5000E0 .750E0
- 21.6700E0 2.000E0
- 8.5500E0 5.000E0
- 62.0000E0 .750E0
- 20.2000E0 2.250E0
- 7.7600E0 3.750E0
- 3.7500E0 5.750E0
- 11.8100E0 3.000E0
- 54.7000E0 .750E0
- 23.7000E0 2.500E0
- 11.5500E0 4.000E0
- 61.3000E0 .750E0
- 17.7000E0 2.500E0
- 8.7400E0 4.000E0
- 59.2000E0 .750E0
- 16.3000E0 2.500E0
- 8.6200E0 4.000E0
- 81.0000E0 .500E0
- 4.8700E0 6.000E0
- 14.6200E0 3.000E0
- 81.7000E0 .500E0
- 17.1700E0 2.750E0
- 81.3000E0 .500E0
- 28.9000E0 1.750E0
+NIST/ITL StRD
+Dataset Name: Chwirut2 (Chwirut2.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 43)
+ Certified Values (lines 41 to 48)
+ Data (lines 61 to 114)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are the result of a NIST study involving
+ ultrasonic calibration. The response variable is
+ ultrasonic response, and the predictor variable is
+ metal distance.
+
+
+
+Reference: Chwirut, D., NIST (197?).
+ Ultrasonic Reference Block Study.
+
+
+
+
+
+Data: 1 Response (y = ultrasonic response)
+ 1 Predictor (x = metal distance)
+ 54 Observations
+ Lower Level of Difficulty
+ Observed Data
+
+Model: Exponential Class
+ 3 Parameters (b1 to b3)
+
+ y = exp(-b1*x)/(b2+b3*x) + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 0.1 0.15 1.6657666537E-01 3.8303286810E-02
+ b2 = 0.01 0.008 5.1653291286E-03 6.6621605126E-04
+ b3 = 0.02 0.010 1.2150007096E-02 1.5304234767E-03
+
+Residual Sum of Squares: 5.1304802941E+02
+Residual Standard Deviation: 3.1717133040E+00
+Degrees of Freedom: 51
+Number of Observations: 54
+
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 92.9000E0 0.500E0
+ 57.1000E0 1.000E0
+ 31.0500E0 1.750E0
+ 11.5875E0 3.750E0
+ 8.0250E0 5.750E0
+ 63.6000E0 0.875E0
+ 21.4000E0 2.250E0
+ 14.2500E0 3.250E0
+ 8.4750E0 5.250E0
+ 63.8000E0 0.750E0
+ 26.8000E0 1.750E0
+ 16.4625E0 2.750E0
+ 7.1250E0 4.750E0
+ 67.3000E0 0.625E0
+ 41.0000E0 1.250E0
+ 21.1500E0 2.250E0
+ 8.1750E0 4.250E0
+ 81.5000E0 .500E0
+ 13.1200E0 3.000E0
+ 59.9000E0 .750E0
+ 14.6200E0 3.000E0
+ 32.9000E0 1.500E0
+ 5.4400E0 6.000E0
+ 12.5600E0 3.000E0
+ 5.4400E0 6.000E0
+ 32.0000E0 1.500E0
+ 13.9500E0 3.000E0
+ 75.8000E0 .500E0
+ 20.0000E0 2.000E0
+ 10.4200E0 4.000E0
+ 59.5000E0 .750E0
+ 21.6700E0 2.000E0
+ 8.5500E0 5.000E0
+ 62.0000E0 .750E0
+ 20.2000E0 2.250E0
+ 7.7600E0 3.750E0
+ 3.7500E0 5.750E0
+ 11.8100E0 3.000E0
+ 54.7000E0 .750E0
+ 23.7000E0 2.500E0
+ 11.5500E0 4.000E0
+ 61.3000E0 .750E0
+ 17.7000E0 2.500E0
+ 8.7400E0 4.000E0
+ 59.2000E0 .750E0
+ 16.3000E0 2.500E0
+ 8.6200E0 4.000E0
+ 81.0000E0 .500E0
+ 4.8700E0 6.000E0
+ 14.6200E0 3.000E0
+ 81.7000E0 .500E0
+ 17.1700E0 2.750E0
+ 81.3000E0 .500E0
+ 28.9000E0 1.750E0
diff --git a/NIST_STRD/DanWood.dat b/NIST_STRD/DanWood.dat
index 479a9bd..317f6a7 100644
--- a/NIST_STRD/DanWood.dat
+++ b/NIST_STRD/DanWood.dat
@@ -1,66 +1,66 @@
-NIST/ITL StRD
-Dataset Name: DanWood (DanWood.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 42)
- Certified Values (lines 41 to 47)
- Data (lines 61 to 66)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data and model are described in Daniel and Wood
- (1980), and originally published in E.S.Keeping,
- "Introduction to Statistical Inference," Van Nostrand
- Company, Princeton, NJ, 1962, p. 354. The response
- variable is energy radieted from a carbon filament
- lamp per cm**2 per second, and the predictor variable
- is the absolute temperature of the filament in 1000
- degrees Kelvin.
-
-Reference: Daniel, C. and F. S. Wood (1980).
- Fitting Equations to Data, Second Edition.
- New York, NY: John Wiley and Sons, pp. 428-431.
-
-
-Data: 1 Response Variable (y = energy)
- 1 Predictor Variable (x = temperature)
- 6 Observations
- Lower Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 2 Parameters (b1 and b2)
-
- y = b1*x**b2 + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1 0.7 7.6886226176E-01 1.8281973860E-02
- b2 = 5 4 3.8604055871E+00 5.1726610913E-02
-
-Residual Sum of Squares: 4.3173084083E-03
-Residual Standard Deviation: 3.2853114039E-02
-Degrees of Freedom: 4
-Number of Observations: 6
-
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 2.138E0 1.309E0
- 3.421E0 1.471E0
- 3.597E0 1.490E0
- 4.340E0 1.565E0
- 4.882E0 1.611E0
- 5.660E0 1.680E0
+NIST/ITL StRD
+Dataset Name: DanWood (DanWood.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 42)
+ Certified Values (lines 41 to 47)
+ Data (lines 61 to 66)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data and model are described in Daniel and Wood
+ (1980), and originally published in E.S.Keeping,
+ "Introduction to Statistical Inference," Van Nostrand
+ Company, Princeton, NJ, 1962, p. 354. The response
+ variable is energy radieted from a carbon filament
+ lamp per cm**2 per second, and the predictor variable
+ is the absolute temperature of the filament in 1000
+ degrees Kelvin.
+
+Reference: Daniel, C. and F. S. Wood (1980).
+ Fitting Equations to Data, Second Edition.
+ New York, NY: John Wiley and Sons, pp. 428-431.
+
+
+Data: 1 Response Variable (y = energy)
+ 1 Predictor Variable (x = temperature)
+ 6 Observations
+ Lower Level of Difficulty
+ Observed Data
+
+Model: Miscellaneous Class
+ 2 Parameters (b1 and b2)
+
+ y = b1*x**b2 + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 1 0.7 7.6886226176E-01 1.8281973860E-02
+ b2 = 5 4 3.8604055871E+00 5.1726610913E-02
+
+Residual Sum of Squares: 4.3173084083E-03
+Residual Standard Deviation: 3.2853114039E-02
+Degrees of Freedom: 4
+Number of Observations: 6
+
+
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 2.138E0 1.309E0
+ 3.421E0 1.471E0
+ 3.597E0 1.490E0
+ 4.340E0 1.565E0
+ 4.882E0 1.611E0
+ 5.660E0 1.680E0
diff --git a/NIST_STRD/ENSO.dat b/NIST_STRD/ENSO.dat
index f374db2..efe5cd8 100644
--- a/NIST_STRD/ENSO.dat
+++ b/NIST_STRD/ENSO.dat
@@ -1,228 +1,228 @@
-NIST/ITL StRD
-Dataset Name: ENSO (ENSO.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 49)
- Certified Values (lines 41 to 54)
- Data (lines 61 to 228)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: The data are monthly averaged atmospheric pressure
- differences between Easter Island and Darwin,
- Australia. This difference drives the trade winds in
- the southern hemisphere. Fourier analysis of the data
- reveals 3 significant cycles. The annual cycle is the
- strongest, but cycles with periods of approximately 44
- and 26 months are also present. These cycles
- correspond to the El Nino and the Southern Oscillation.
- Arguments to the SIN and COS functions are in radians.
-
-Reference: Kahaner, D., C. Moler, and S. Nash, (1989).
- Numerical Methods and Software.
- Englewood Cliffs, NJ: Prentice Hall, pp. 441-445.
-
-Data: 1 Response (y = atmospheric pressure)
- 1 Predictor (x = time)
- 168 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 9 Parameters (b1 to b9)
-
- y = b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 )
- + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 )
- + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ) + e
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 11.0 10.0 1.0510749193E+01 1.7488832467E-01
- b2 = 3.0 3.0 3.0762128085E+00 2.4310052139E-01
- b3 = 0.5 0.5 5.3280138227E-01 2.4354686618E-01
- b4 = 40.0 44.0 4.4311088700E+01 9.4408025976E-01
- b5 = -0.7 -1.5 -1.6231428586E+00 2.8078369611E-01
- b6 = -1.3 0.5 5.2554493756E-01 4.8073701119E-01
- b7 = 25.0 26.0 2.6887614440E+01 4.1612939130E-01
- b8 = -0.3 -0.1 2.1232288488E-01 5.1460022911E-01
- b9 = 1.4 1.5 1.4966870418E+00 2.5434468893E-01
-
-Residual Sum of Squares: 7.8853978668E+02
-Residual Standard Deviation: 2.2269642403E+00
-Degrees of Freedom: 159
-Number of Observations: 168
-
-
-
-
-
-Data: y x
- 12.90000 1.000000
- 11.30000 2.000000
- 10.60000 3.000000
- 11.20000 4.000000
- 10.90000 5.000000
- 7.500000 6.000000
- 7.700000 7.000000
- 11.70000 8.000000
- 12.90000 9.000000
- 14.30000 10.000000
- 10.90000 11.00000
- 13.70000 12.00000
- 17.10000 13.00000
- 14.00000 14.00000
- 15.30000 15.00000
- 8.500000 16.00000
- 5.700000 17.00000
- 5.500000 18.00000
- 7.600000 19.00000
- 8.600000 20.00000
- 7.300000 21.00000
- 7.600000 22.00000
- 12.70000 23.00000
- 11.00000 24.00000
- 12.70000 25.00000
- 12.90000 26.00000
- 13.00000 27.00000
- 10.90000 28.00000
- 10.400000 29.00000
- 10.200000 30.00000
- 8.000000 31.00000
- 10.90000 32.00000
- 13.60000 33.00000
- 10.500000 34.00000
- 9.200000 35.00000
- 12.40000 36.00000
- 12.70000 37.00000
- 13.30000 38.00000
- 10.100000 39.00000
- 7.800000 40.00000
- 4.800000 41.00000
- 3.000000 42.00000
- 2.500000 43.00000
- 6.300000 44.00000
- 9.700000 45.00000
- 11.60000 46.00000
- 8.600000 47.00000
- 12.40000 48.00000
- 10.500000 49.00000
- 13.30000 50.00000
- 10.400000 51.00000
- 8.100000 52.00000
- 3.700000 53.00000
- 10.70000 54.00000
- 5.100000 55.00000
- 10.400000 56.00000
- 10.90000 57.00000
- 11.70000 58.00000
- 11.40000 59.00000
- 13.70000 60.00000
- 14.10000 61.00000
- 14.00000 62.00000
- 12.50000 63.00000
- 6.300000 64.00000
- 9.600000 65.00000
- 11.70000 66.00000
- 5.000000 67.00000
- 10.80000 68.00000
- 12.70000 69.00000
- 10.80000 70.00000
- 11.80000 71.00000
- 12.60000 72.00000
- 15.70000 73.00000
- 12.60000 74.00000
- 14.80000 75.00000
- 7.800000 76.00000
- 7.100000 77.00000
- 11.20000 78.00000
- 8.100000 79.00000
- 6.400000 80.00000
- 5.200000 81.00000
- 12.00000 82.00000
- 10.200000 83.00000
- 12.70000 84.00000
- 10.200000 85.00000
- 14.70000 86.00000
- 12.20000 87.00000
- 7.100000 88.00000
- 5.700000 89.00000
- 6.700000 90.00000
- 3.900000 91.00000
- 8.500000 92.00000
- 8.300000 93.00000
- 10.80000 94.00000
- 16.70000 95.00000
- 12.60000 96.00000
- 12.50000 97.00000
- 12.50000 98.00000
- 9.800000 99.00000
- 7.200000 100.00000
- 4.100000 101.00000
- 10.60000 102.00000
- 10.100000 103.00000
- 10.100000 104.00000
- 11.90000 105.00000
- 13.60000 106.0000
- 16.30000 107.0000
- 17.60000 108.0000
- 15.50000 109.0000
- 16.00000 110.0000
- 15.20000 111.0000
- 11.20000 112.0000
- 14.30000 113.0000
- 14.50000 114.0000
- 8.500000 115.0000
- 12.00000 116.0000
- 12.70000 117.0000
- 11.30000 118.0000
- 14.50000 119.0000
- 15.10000 120.0000
- 10.400000 121.0000
- 11.50000 122.0000
- 13.40000 123.0000
- 7.500000 124.0000
- 0.6000000 125.0000
- 0.3000000 126.0000
- 5.500000 127.0000
- 5.000000 128.0000
- 4.600000 129.0000
- 8.200000 130.0000
- 9.900000 131.0000
- 9.200000 132.0000
- 12.50000 133.0000
- 10.90000 134.0000
- 9.900000 135.0000
- 8.900000 136.0000
- 7.600000 137.0000
- 9.500000 138.0000
- 8.400000 139.0000
- 10.70000 140.0000
- 13.60000 141.0000
- 13.70000 142.0000
- 13.70000 143.0000
- 16.50000 144.0000
- 16.80000 145.0000
- 17.10000 146.0000
- 15.40000 147.0000
- 9.500000 148.0000
- 6.100000 149.0000
- 10.100000 150.0000
- 9.300000 151.0000
- 5.300000 152.0000
- 11.20000 153.0000
- 16.60000 154.0000
- 15.60000 155.0000
- 12.00000 156.0000
- 11.50000 157.0000
- 8.600000 158.0000
- 13.80000 159.0000
- 8.700000 160.0000
- 8.600000 161.0000
- 8.600000 162.0000
- 8.700000 163.0000
- 12.80000 164.0000
- 13.20000 165.0000
- 14.00000 166.0000
- 13.40000 167.0000
- 14.80000 168.0000
+NIST/ITL StRD
+Dataset Name: ENSO (ENSO.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 49)
+ Certified Values (lines 41 to 54)
+ Data (lines 61 to 228)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: The data are monthly averaged atmospheric pressure
+ differences between Easter Island and Darwin,
+ Australia. This difference drives the trade winds in
+ the southern hemisphere. Fourier analysis of the data
+ reveals 3 significant cycles. The annual cycle is the
+ strongest, but cycles with periods of approximately 44
+ and 26 months are also present. These cycles
+ correspond to the El Nino and the Southern Oscillation.
+ Arguments to the SIN and COS functions are in radians.
+
+Reference: Kahaner, D., C. Moler, and S. Nash, (1989).
+ Numerical Methods and Software.
+ Englewood Cliffs, NJ: Prentice Hall, pp. 441-445.
+
+Data: 1 Response (y = atmospheric pressure)
+ 1 Predictor (x = time)
+ 168 Observations
+ Average Level of Difficulty
+ Observed Data
+
+Model: Miscellaneous Class
+ 9 Parameters (b1 to b9)
+
+ y = b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 )
+ + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 )
+ + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ) + e
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 11.0 10.0 1.0510749193E+01 1.7488832467E-01
+ b2 = 3.0 3.0 3.0762128085E+00 2.4310052139E-01
+ b3 = 0.5 0.5 5.3280138227E-01 2.4354686618E-01
+ b4 = 40.0 44.0 4.4311088700E+01 9.4408025976E-01
+ b5 = -0.7 -1.5 -1.6231428586E+00 2.8078369611E-01
+ b6 = -1.3 0.5 5.2554493756E-01 4.8073701119E-01
+ b7 = 25.0 26.0 2.6887614440E+01 4.1612939130E-01
+ b8 = -0.3 -0.1 2.1232288488E-01 5.1460022911E-01
+ b9 = 1.4 1.5 1.4966870418E+00 2.5434468893E-01
+
+Residual Sum of Squares: 7.8853978668E+02
+Residual Standard Deviation: 2.2269642403E+00
+Degrees of Freedom: 159
+Number of Observations: 168
+
+
+
+
+
+Data: y x
+ 12.90000 1.000000
+ 11.30000 2.000000
+ 10.60000 3.000000
+ 11.20000 4.000000
+ 10.90000 5.000000
+ 7.500000 6.000000
+ 7.700000 7.000000
+ 11.70000 8.000000
+ 12.90000 9.000000
+ 14.30000 10.000000
+ 10.90000 11.00000
+ 13.70000 12.00000
+ 17.10000 13.00000
+ 14.00000 14.00000
+ 15.30000 15.00000
+ 8.500000 16.00000
+ 5.700000 17.00000
+ 5.500000 18.00000
+ 7.600000 19.00000
+ 8.600000 20.00000
+ 7.300000 21.00000
+ 7.600000 22.00000
+ 12.70000 23.00000
+ 11.00000 24.00000
+ 12.70000 25.00000
+ 12.90000 26.00000
+ 13.00000 27.00000
+ 10.90000 28.00000
+ 10.400000 29.00000
+ 10.200000 30.00000
+ 8.000000 31.00000
+ 10.90000 32.00000
+ 13.60000 33.00000
+ 10.500000 34.00000
+ 9.200000 35.00000
+ 12.40000 36.00000
+ 12.70000 37.00000
+ 13.30000 38.00000
+ 10.100000 39.00000
+ 7.800000 40.00000
+ 4.800000 41.00000
+ 3.000000 42.00000
+ 2.500000 43.00000
+ 6.300000 44.00000
+ 9.700000 45.00000
+ 11.60000 46.00000
+ 8.600000 47.00000
+ 12.40000 48.00000
+ 10.500000 49.00000
+ 13.30000 50.00000
+ 10.400000 51.00000
+ 8.100000 52.00000
+ 3.700000 53.00000
+ 10.70000 54.00000
+ 5.100000 55.00000
+ 10.400000 56.00000
+ 10.90000 57.00000
+ 11.70000 58.00000
+ 11.40000 59.00000
+ 13.70000 60.00000
+ 14.10000 61.00000
+ 14.00000 62.00000
+ 12.50000 63.00000
+ 6.300000 64.00000
+ 9.600000 65.00000
+ 11.70000 66.00000
+ 5.000000 67.00000
+ 10.80000 68.00000
+ 12.70000 69.00000
+ 10.80000 70.00000
+ 11.80000 71.00000
+ 12.60000 72.00000
+ 15.70000 73.00000
+ 12.60000 74.00000
+ 14.80000 75.00000
+ 7.800000 76.00000
+ 7.100000 77.00000
+ 11.20000 78.00000
+ 8.100000 79.00000
+ 6.400000 80.00000
+ 5.200000 81.00000
+ 12.00000 82.00000
+ 10.200000 83.00000
+ 12.70000 84.00000
+ 10.200000 85.00000
+ 14.70000 86.00000
+ 12.20000 87.00000
+ 7.100000 88.00000
+ 5.700000 89.00000
+ 6.700000 90.00000
+ 3.900000 91.00000
+ 8.500000 92.00000
+ 8.300000 93.00000
+ 10.80000 94.00000
+ 16.70000 95.00000
+ 12.60000 96.00000
+ 12.50000 97.00000
+ 12.50000 98.00000
+ 9.800000 99.00000
+ 7.200000 100.00000
+ 4.100000 101.00000
+ 10.60000 102.00000
+ 10.100000 103.00000
+ 10.100000 104.00000
+ 11.90000 105.00000
+ 13.60000 106.0000
+ 16.30000 107.0000
+ 17.60000 108.0000
+ 15.50000 109.0000
+ 16.00000 110.0000
+ 15.20000 111.0000
+ 11.20000 112.0000
+ 14.30000 113.0000
+ 14.50000 114.0000
+ 8.500000 115.0000
+ 12.00000 116.0000
+ 12.70000 117.0000
+ 11.30000 118.0000
+ 14.50000 119.0000
+ 15.10000 120.0000
+ 10.400000 121.0000
+ 11.50000 122.0000
+ 13.40000 123.0000
+ 7.500000 124.0000
+ 0.6000000 125.0000
+ 0.3000000 126.0000
+ 5.500000 127.0000
+ 5.000000 128.0000
+ 4.600000 129.0000
+ 8.200000 130.0000
+ 9.900000 131.0000
+ 9.200000 132.0000
+ 12.50000 133.0000
+ 10.90000 134.0000
+ 9.900000 135.0000
+ 8.900000 136.0000
+ 7.600000 137.0000
+ 9.500000 138.0000
+ 8.400000 139.0000
+ 10.70000 140.0000
+ 13.60000 141.0000
+ 13.70000 142.0000
+ 13.70000 143.0000
+ 16.50000 144.0000
+ 16.80000 145.0000
+ 17.10000 146.0000
+ 15.40000 147.0000
+ 9.500000 148.0000
+ 6.100000 149.0000
+ 10.100000 150.0000
+ 9.300000 151.0000
+ 5.300000 152.0000
+ 11.20000 153.0000
+ 16.60000 154.0000
+ 15.60000 155.0000
+ 12.00000 156.0000
+ 11.50000 157.0000
+ 8.600000 158.0000
+ 13.80000 159.0000
+ 8.700000 160.0000
+ 8.600000 161.0000
+ 8.600000 162.0000
+ 8.700000 163.0000
+ 12.80000 164.0000
+ 13.20000 165.0000
+ 14.00000 166.0000
+ 13.40000 167.0000
+ 14.80000 168.0000
diff --git a/NIST_STRD/Eckerle4.dat b/NIST_STRD/Eckerle4.dat
index 2d0d8bf..dd54f5a 100644
--- a/NIST_STRD/Eckerle4.dat
+++ b/NIST_STRD/Eckerle4.dat
@@ -1,95 +1,95 @@
-NIST/ITL StRD
-Dataset Name: Eckerle4 (Eckerle4.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 95)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- circular interference transmittance. The response
- variable is transmittance, and the predictor variable
- is wavelength.
-
-
-Reference: Eckerle, K., NIST (197?).
- Circular Interference Transmittance Study.
-
-
-
-
-
-
-Data: 1 Response Variable (y = transmittance)
- 1 Predictor Variable (x = wavelength)
- 35 Observations
- Higher Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 3 Parameters (b1 to b3)
-
- y = (b1/b2) * exp[-0.5*((x-b3)/b2)**2] + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1 1.5 1.5543827178E+00 1.5408051163E-02
- b2 = 10 5 4.0888321754E+00 4.6803020753E-02
- b3 = 500 450 4.5154121844E+02 4.6800518816E-02
-
-Residual Sum of Squares: 1.4635887487E-03
-Residual Standard Deviation: 6.7629245447E-03
-Degrees of Freedom: 32
-Number of Observations: 35
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 0.0001575E0 400.000000E0
- 0.0001699E0 405.000000E0
- 0.0002350E0 410.000000E0
- 0.0003102E0 415.000000E0
- 0.0004917E0 420.000000E0
- 0.0008710E0 425.000000E0
- 0.0017418E0 430.000000E0
- 0.0046400E0 435.000000E0
- 0.0065895E0 436.500000E0
- 0.0097302E0 438.000000E0
- 0.0149002E0 439.500000E0
- 0.0237310E0 441.000000E0
- 0.0401683E0 442.500000E0
- 0.0712559E0 444.000000E0
- 0.1264458E0 445.500000E0
- 0.2073413E0 447.000000E0
- 0.2902366E0 448.500000E0
- 0.3445623E0 450.000000E0
- 0.3698049E0 451.500000E0
- 0.3668534E0 453.000000E0
- 0.3106727E0 454.500000E0
- 0.2078154E0 456.000000E0
- 0.1164354E0 457.500000E0
- 0.0616764E0 459.000000E0
- 0.0337200E0 460.500000E0
- 0.0194023E0 462.000000E0
- 0.0117831E0 463.500000E0
- 0.0074357E0 465.000000E0
- 0.0022732E0 470.000000E0
- 0.0008800E0 475.000000E0
- 0.0004579E0 480.000000E0
- 0.0002345E0 485.000000E0
- 0.0001586E0 490.000000E0
- 0.0001143E0 495.000000E0
- 0.0000710E0 500.000000E0
+NIST/ITL StRD
+Dataset Name: Eckerle4 (Eckerle4.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 43)
+ Certified Values (lines 41 to 48)
+ Data (lines 61 to 95)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are the result of a NIST study involving
+ circular interference transmittance. The response
+ variable is transmittance, and the predictor variable
+ is wavelength.
+
+
+Reference: Eckerle, K., NIST (197?).
+ Circular Interference Transmittance Study.
+
+
+
+
+
+
+Data: 1 Response Variable (y = transmittance)
+ 1 Predictor Variable (x = wavelength)
+ 35 Observations
+ Higher Level of Difficulty
+ Observed Data
+
+Model: Exponential Class
+ 3 Parameters (b1 to b3)
+
+ y = (b1/b2) * exp[-0.5*((x-b3)/b2)**2] + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 1 1.5 1.5543827178E+00 1.5408051163E-02
+ b2 = 10 5 4.0888321754E+00 4.6803020753E-02
+ b3 = 500 450 4.5154121844E+02 4.6800518816E-02
+
+Residual Sum of Squares: 1.4635887487E-03
+Residual Standard Deviation: 6.7629245447E-03
+Degrees of Freedom: 32
+Number of Observations: 35
+
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 0.0001575E0 400.000000E0
+ 0.0001699E0 405.000000E0
+ 0.0002350E0 410.000000E0
+ 0.0003102E0 415.000000E0
+ 0.0004917E0 420.000000E0
+ 0.0008710E0 425.000000E0
+ 0.0017418E0 430.000000E0
+ 0.0046400E0 435.000000E0
+ 0.0065895E0 436.500000E0
+ 0.0097302E0 438.000000E0
+ 0.0149002E0 439.500000E0
+ 0.0237310E0 441.000000E0
+ 0.0401683E0 442.500000E0
+ 0.0712559E0 444.000000E0
+ 0.1264458E0 445.500000E0
+ 0.2073413E0 447.000000E0
+ 0.2902366E0 448.500000E0
+ 0.3445623E0 450.000000E0
+ 0.3698049E0 451.500000E0
+ 0.3668534E0 453.000000E0
+ 0.3106727E0 454.500000E0
+ 0.2078154E0 456.000000E0
+ 0.1164354E0 457.500000E0
+ 0.0616764E0 459.000000E0
+ 0.0337200E0 460.500000E0
+ 0.0194023E0 462.000000E0
+ 0.0117831E0 463.500000E0
+ 0.0074357E0 465.000000E0
+ 0.0022732E0 470.000000E0
+ 0.0008800E0 475.000000E0
+ 0.0004579E0 480.000000E0
+ 0.0002345E0 485.000000E0
+ 0.0001586E0 490.000000E0
+ 0.0001143E0 495.000000E0
+ 0.0000710E0 500.000000E0
diff --git a/NIST_STRD/Gauss1.dat b/NIST_STRD/Gauss1.dat
index df8dfac..89c389e 100644
--- a/NIST_STRD/Gauss1.dat
+++ b/NIST_STRD/Gauss1.dat
@@ -1,310 +1,310 @@
-NIST/ITL StRD
-Dataset Name: Gauss1 (Gauss1.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 48)
- Certified Values (lines 41 to 53)
- Data (lines 61 to 310)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: The data are two well-separated Gaussians on a
- decaying exponential baseline plus normally
- distributed zero-mean noise with variance = 6.25.
-
-Reference: Rust, B., NIST (1996).
-
-
-
-
-
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 250 Observations
- Lower Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 8 Parameters (b1 to b8)
-
- y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
- + b6*exp( -(x-b7)**2 / b8**2 ) + e
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 97.0 94.0 9.8778210871E+01 5.7527312730E-01
- b2 = 0.009 0.0105 1.0497276517E-02 1.1406289017E-04
- b3 = 100.0 99.0 1.0048990633E+02 5.8831775752E-01
- b4 = 65.0 63.0 6.7481111276E+01 1.0460593412E-01
- b5 = 20.0 25.0 2.3129773360E+01 1.7439951146E-01
- b6 = 70.0 71.0 7.1994503004E+01 6.2622793913E-01
- b7 = 178.0 180.0 1.7899805021E+02 1.2436988217E-01
- b8 = 16.5 20.0 1.8389389025E+01 2.0134312832E-01
-
-Residual Sum of Squares: 1.3158222432E+03
-Residual Standard Deviation: 2.3317980180E+00
-Degrees of Freedom: 242
-Number of Observations: 250
-
-
-
-
-
-
-Data: y x
- 97.62227 1.000000
- 97.80724 2.000000
- 96.62247 3.000000
- 92.59022 4.000000
- 91.23869 5.000000
- 95.32704 6.000000
- 90.35040 7.000000
- 89.46235 8.000000
- 91.72520 9.000000
- 89.86916 10.000000
- 86.88076 11.00000
- 85.94360 12.00000
- 87.60686 13.00000
- 86.25839 14.00000
- 80.74976 15.00000
- 83.03551 16.00000
- 88.25837 17.00000
- 82.01316 18.00000
- 82.74098 19.00000
- 83.30034 20.00000
- 81.27850 21.00000
- 81.85506 22.00000
- 80.75195 23.00000
- 80.09573 24.00000
- 81.07633 25.00000
- 78.81542 26.00000
- 78.38596 27.00000
- 79.93386 28.00000
- 79.48474 29.00000
- 79.95942 30.00000
- 76.10691 31.00000
- 78.39830 32.00000
- 81.43060 33.00000
- 82.48867 34.00000
- 81.65462 35.00000
- 80.84323 36.00000
- 88.68663 37.00000
- 84.74438 38.00000
- 86.83934 39.00000
- 85.97739 40.00000
- 91.28509 41.00000
- 97.22411 42.00000
- 93.51733 43.00000
- 94.10159 44.00000
- 101.91760 45.00000
- 98.43134 46.00000
- 110.4214 47.00000
- 107.6628 48.00000
- 111.7288 49.00000
- 116.5115 50.00000
- 120.7609 51.00000
- 123.9553 52.00000
- 124.2437 53.00000
- 130.7996 54.00000
- 133.2960 55.00000
- 130.7788 56.00000
- 132.0565 57.00000
- 138.6584 58.00000
- 142.9252 59.00000
- 142.7215 60.00000
- 144.1249 61.00000
- 147.4377 62.00000
- 148.2647 63.00000
- 152.0519 64.00000
- 147.3863 65.00000
- 149.2074 66.00000
- 148.9537 67.00000
- 144.5876 68.00000
- 148.1226 69.00000
- 148.0144 70.00000
- 143.8893 71.00000
- 140.9088 72.00000
- 143.4434 73.00000
- 139.3938 74.00000
- 135.9878 75.00000
- 136.3927 76.00000
- 126.7262 77.00000
- 124.4487 78.00000
- 122.8647 79.00000
- 113.8557 80.00000
- 113.7037 81.00000
- 106.8407 82.00000
- 107.0034 83.00000
- 102.46290 84.00000
- 96.09296 85.00000
- 94.57555 86.00000
- 86.98824 87.00000
- 84.90154 88.00000
- 81.18023 89.00000
- 76.40117 90.00000
- 67.09200 91.00000
- 72.67155 92.00000
- 68.10848 93.00000
- 67.99088 94.00000
- 63.34094 95.00000
- 60.55253 96.00000
- 56.18687 97.00000
- 53.64482 98.00000
- 53.70307 99.00000
- 48.07893 100.00000
- 42.21258 101.00000
- 45.65181 102.00000
- 41.69728 103.00000
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- 39.21349 105.00000
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- 36.68395 107.0000
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- 32.64648 111.0000
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- 26.90045 142.0000
- 25.39919 143.0000
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- 23.76039 145.0000
- 25.89689 146.0000
- 27.64231 147.0000
- 22.86101 148.0000
- 26.47003 149.0000
- 23.72888 150.0000
- 27.54334 151.0000
- 30.52683 152.0000
- 28.07261 153.0000
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- 35.41207 157.0000
- 37.09336 158.0000
- 40.98330 159.0000
- 39.53923 160.0000
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- 47.46305 162.0000
- 51.04166 163.0000
- 54.58065 164.0000
- 57.53001 165.0000
- 61.42089 166.0000
- 62.79032 167.0000
- 68.51455 168.0000
- 70.23053 169.0000
- 74.42776 170.0000
- 76.59911 171.0000
- 81.62053 172.0000
- 83.42208 173.0000
- 79.17451 174.0000
- 88.56985 175.0000
- 85.66525 176.0000
- 86.55502 177.0000
- 90.65907 178.0000
- 84.27290 179.0000
- 85.72220 180.0000
- 83.10702 181.0000
- 82.16884 182.0000
- 80.42568 183.0000
- 78.15692 184.0000
- 79.79691 185.0000
- 77.84378 186.0000
- 74.50327 187.0000
- 71.57289 188.0000
- 65.88031 189.0000
- 65.01385 190.0000
- 60.19582 191.0000
- 59.66726 192.0000
- 52.95478 193.0000
- 53.87792 194.0000
- 44.91274 195.0000
- 41.09909 196.0000
- 41.68018 197.0000
- 34.53379 198.0000
- 34.86419 199.0000
- 33.14787 200.0000
- 29.58864 201.0000
- 27.29462 202.0000
- 21.91439 203.0000
- 19.08159 204.0000
- 24.90290 205.0000
- 19.82341 206.0000
- 16.75551 207.0000
- 18.24558 208.0000
- 17.23549 209.0000
- 16.34934 210.0000
- 13.71285 211.0000
- 14.75676 212.0000
- 13.97169 213.0000
- 12.42867 214.0000
- 14.35519 215.0000
- 7.703309 216.0000
- 10.234410 217.0000
- 11.78315 218.0000
- 13.87768 219.0000
- 4.535700 220.0000
- 10.059280 221.0000
- 8.424824 222.0000
- 10.533120 223.0000
- 9.602255 224.0000
- 7.877514 225.0000
- 6.258121 226.0000
- 8.899865 227.0000
- 7.877754 228.0000
- 12.51191 229.0000
- 10.66205 230.0000
- 6.035400 231.0000
- 6.790655 232.0000
- 8.783535 233.0000
- 4.600288 234.0000
- 8.400915 235.0000
- 7.216561 236.0000
- 10.017410 237.0000
- 7.331278 238.0000
- 6.527863 239.0000
- 2.842001 240.0000
- 10.325070 241.0000
- 4.790995 242.0000
- 8.377101 243.0000
- 6.264445 244.0000
- 2.706213 245.0000
- 8.362329 246.0000
- 8.983658 247.0000
- 3.362571 248.0000
- 1.182746 249.0000
- 4.875359 250.0000
+NIST/ITL StRD
+Dataset Name: Gauss1 (Gauss1.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 48)
+ Certified Values (lines 41 to 53)
+ Data (lines 61 to 310)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: The data are two well-separated Gaussians on a
+ decaying exponential baseline plus normally
+ distributed zero-mean noise with variance = 6.25.
+
+Reference: Rust, B., NIST (1996).
+
+
+
+
+
+
+
+
+
+Data: 1 Response (y)
+ 1 Predictor (x)
+ 250 Observations
+ Lower Level of Difficulty
+ Generated Data
+
+Model: Exponential Class
+ 8 Parameters (b1 to b8)
+
+ y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
+ + b6*exp( -(x-b7)**2 / b8**2 ) + e
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 97.0 94.0 9.8778210871E+01 5.7527312730E-01
+ b2 = 0.009 0.0105 1.0497276517E-02 1.1406289017E-04
+ b3 = 100.0 99.0 1.0048990633E+02 5.8831775752E-01
+ b4 = 65.0 63.0 6.7481111276E+01 1.0460593412E-01
+ b5 = 20.0 25.0 2.3129773360E+01 1.7439951146E-01
+ b6 = 70.0 71.0 7.1994503004E+01 6.2622793913E-01
+ b7 = 178.0 180.0 1.7899805021E+02 1.2436988217E-01
+ b8 = 16.5 20.0 1.8389389025E+01 2.0134312832E-01
+
+Residual Sum of Squares: 1.3158222432E+03
+Residual Standard Deviation: 2.3317980180E+00
+Degrees of Freedom: 242
+Number of Observations: 250
+
+
+
+
+
+
+Data: y x
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diff --git a/NIST_STRD/Gauss2.dat b/NIST_STRD/Gauss2.dat
index 38222eb..ff185d1 100644
--- a/NIST_STRD/Gauss2.dat
+++ b/NIST_STRD/Gauss2.dat
@@ -1,310 +1,310 @@
-NIST/ITL StRD
-Dataset Name: Gauss2 (Gauss2.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 48)
- Certified Values (lines 41 to 53)
- Data (lines 61 to 310)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: The data are two slightly-blended Gaussians on a
- decaying exponential baseline plus normally
- distributed zero-mean noise with variance = 6.25.
-
-Reference: Rust, B., NIST (1996).
-
-
-
-
-
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 250 Observations
- Lower Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 8 Parameters (b1 to b8)
-
- y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
- + b6*exp( -(x-b7)**2 / b8**2 ) + e
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 96.0 98.0 9.9018328406E+01 5.3748766879E-01
- b2 = 0.009 0.0105 1.0994945399E-02 1.3335306766E-04
- b3 = 103.0 103.0 1.0188022528E+02 5.9217315772E-01
- b4 = 106.0 105.0 1.0703095519E+02 1.5006798316E-01
- b5 = 18.0 20.0 2.3578584029E+01 2.2695595067E-01
- b6 = 72.0 73.0 7.2045589471E+01 6.1721965884E-01
- b7 = 151.0 150.0 1.5327010194E+02 1.9466674341E-01
- b8 = 18.0 20.0 1.9525972636E+01 2.6416549393E-01
-
-Residual Sum of Squares: 1.2475282092E+03
-Residual Standard Deviation: 2.2704790782E+00
-Degrees of Freedom: 242
-Number of Observations: 250
-
-
-
-
-
-
-Data: y x
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- 1.182678 249.0000
- 4.875312 250.0000
+NIST/ITL StRD
+Dataset Name: Gauss2 (Gauss2.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 48)
+ Certified Values (lines 41 to 53)
+ Data (lines 61 to 310)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: The data are two slightly-blended Gaussians on a
+ decaying exponential baseline plus normally
+ distributed zero-mean noise with variance = 6.25.
+
+Reference: Rust, B., NIST (1996).
+
+
+
+
+
+
+
+
+
+Data: 1 Response (y)
+ 1 Predictor (x)
+ 250 Observations
+ Lower Level of Difficulty
+ Generated Data
+
+Model: Exponential Class
+ 8 Parameters (b1 to b8)
+
+ y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
+ + b6*exp( -(x-b7)**2 / b8**2 ) + e
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 96.0 98.0 9.9018328406E+01 5.3748766879E-01
+ b2 = 0.009 0.0105 1.0994945399E-02 1.3335306766E-04
+ b3 = 103.0 103.0 1.0188022528E+02 5.9217315772E-01
+ b4 = 106.0 105.0 1.0703095519E+02 1.5006798316E-01
+ b5 = 18.0 20.0 2.3578584029E+01 2.2695595067E-01
+ b6 = 72.0 73.0 7.2045589471E+01 6.1721965884E-01
+ b7 = 151.0 150.0 1.5327010194E+02 1.9466674341E-01
+ b8 = 18.0 20.0 1.9525972636E+01 2.6416549393E-01
+
+Residual Sum of Squares: 1.2475282092E+03
+Residual Standard Deviation: 2.2704790782E+00
+Degrees of Freedom: 242
+Number of Observations: 250
+
+
+
+
+
+
+Data: y x
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diff --git a/NIST_STRD/Gauss3.dat b/NIST_STRD/Gauss3.dat
index e5eb56d..0f880b0 100644
--- a/NIST_STRD/Gauss3.dat
+++ b/NIST_STRD/Gauss3.dat
@@ -1,310 +1,310 @@
-NIST/ITL StRD
-Dataset Name: Gauss3 (Gauss3.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 48)
- Certified Values (lines 41 to 53)
- Data (lines 61 to 310)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: The data are two strongly-blended Gaussians on a
- decaying exponential baseline plus normally
- distributed zero-mean noise with variance = 6.25.
-
-Reference: Rust, B., NIST (1996).
-
-
-
-
-
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 250 Observations
- Average Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 8 Parameters (b1 to b8)
-
- y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
- + b6*exp( -(x-b7)**2 / b8**2 ) + e
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 94.9 96.0 9.8940368970E+01 5.3005192833E-01
- b2 = 0.009 0.0096 1.0945879335E-02 1.2554058911E-04
- b3 = 90.1 80.0 1.0069553078E+02 8.1256587317E-01
- b4 = 113.0 110.0 1.1163619459E+02 3.5317859757E-01
- b5 = 20.0 25.0 2.3300500029E+01 3.6584783023E-01
- b6 = 73.8 74.0 7.3705031418E+01 1.2091239082E+00
- b7 = 140.0 139.0 1.4776164251E+02 4.0488183351E-01
- b8 = 20.0 25.0 1.9668221230E+01 3.7806634336E-01
-
-Residual Sum of Squares: 1.2444846360E+03
-Residual Standard Deviation: 2.2677077625E+00
-Degrees of Freedom: 242
-Number of Observations: 250
-
-
-
-
-
-
-Data: y x
- 97.58776 1.000000
- 97.76344 2.000000
- 96.56705 3.000000
- 92.52037 4.000000
- 91.15097 5.000000
- 95.21728 6.000000
- 90.21355 7.000000
- 89.29235 8.000000
- 91.51479 9.000000
- 89.60965 10.000000
- 86.56187 11.00000
- 85.55315 12.00000
- 87.13053 13.00000
- 85.67938 14.00000
- 80.04849 15.00000
- 82.18922 16.00000
- 87.24078 17.00000
- 80.79401 18.00000
- 81.28564 19.00000
- 81.56932 20.00000
- 79.22703 21.00000
- 79.43259 22.00000
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- 76.75438 24.00000
- 77.17338 25.00000
- 74.27296 26.00000
- 73.11830 27.00000
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- 13.09591 219.0000
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- 10.61601 230.0000
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- 10.012090 237.0000
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- 8.362109 246.0000
- 8.983507 247.0000
- 3.362469 248.0000
- 1.182678 249.0000
- 4.875312 250.0000
+NIST/ITL StRD
+Dataset Name: Gauss3 (Gauss3.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 48)
+ Certified Values (lines 41 to 53)
+ Data (lines 61 to 310)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: The data are two strongly-blended Gaussians on a
+ decaying exponential baseline plus normally
+ distributed zero-mean noise with variance = 6.25.
+
+Reference: Rust, B., NIST (1996).
+
+
+
+
+
+
+
+
+
+Data: 1 Response (y)
+ 1 Predictor (x)
+ 250 Observations
+ Average Level of Difficulty
+ Generated Data
+
+Model: Exponential Class
+ 8 Parameters (b1 to b8)
+
+ y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
+ + b6*exp( -(x-b7)**2 / b8**2 ) + e
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 94.9 96.0 9.8940368970E+01 5.3005192833E-01
+ b2 = 0.009 0.0096 1.0945879335E-02 1.2554058911E-04
+ b3 = 90.1 80.0 1.0069553078E+02 8.1256587317E-01
+ b4 = 113.0 110.0 1.1163619459E+02 3.5317859757E-01
+ b5 = 20.0 25.0 2.3300500029E+01 3.6584783023E-01
+ b6 = 73.8 74.0 7.3705031418E+01 1.2091239082E+00
+ b7 = 140.0 139.0 1.4776164251E+02 4.0488183351E-01
+ b8 = 20.0 25.0 1.9668221230E+01 3.7806634336E-01
+
+Residual Sum of Squares: 1.2444846360E+03
+Residual Standard Deviation: 2.2677077625E+00
+Degrees of Freedom: 242
+Number of Observations: 250
+
+
+
+
+
+
+Data: y x
+ 97.58776 1.000000
+ 97.76344 2.000000
+ 96.56705 3.000000
+ 92.52037 4.000000
+ 91.15097 5.000000
+ 95.21728 6.000000
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diff --git a/NIST_STRD/Hahn1.dat b/NIST_STRD/Hahn1.dat
index f3069d7..0e493a4 100644
--- a/NIST_STRD/Hahn1.dat
+++ b/NIST_STRD/Hahn1.dat
@@ -1,296 +1,296 @@
-NIST/ITL StRD
-Dataset Name: Hahn1 (Hahn1.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 47)
- Certified Values (lines 41 to 52)
- Data (lines 61 to 296)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- the thermal expansion of copper. The response
- variable is the coefficient of thermal expansion, and
- the predictor variable is temperature in degrees
- kelvin.
-
-
-Reference: Hahn, T., NIST (197?).
- Copper Thermal Expansion Study.
-
-
-
-
-
-Data: 1 Response (y = coefficient of thermal expansion)
- 1 Predictor (x = temperature, degrees kelvin)
- 236 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Rational Class (cubic/cubic)
- 7 Parameters (b1 to b7)
-
- y = (b1+b2*x+b3*x**2+b4*x**3) /
- (1+b5*x+b6*x**2+b7*x**3) + e
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 10 1 1.0776351733E+00 1.7070154742E-01
- b2 = -1 -0.1 -1.2269296921E-01 1.2000289189E-02
- b3 = 0.05 0.005 4.0863750610E-03 2.2508314937E-04
- b4 = -0.00001 -0.000001 -1.4262662514E-06 2.7578037666E-07
- b5 = -0.05 -0.005 -5.7609940901E-03 2.4712888219E-04
- b6 = 0.001 0.0001 2.4053735503E-04 1.0449373768E-05
- b7 = -0.000001 -0.0000001 -1.2314450199E-07 1.3027335327E-08
-
-Residual Sum of Squares: 1.5324382854E+00
-Residual Standard Deviation: 8.1803852243E-02
-Degrees of Freedom: 229
-Number of Observations: 236
-
-
-
-
-
-
-
-Data: y x
- .591E0 24.41E0
- 1.547E0 34.82E0
- 2.902E0 44.09E0
- 2.894E0 45.07E0
- 4.703E0 54.98E0
- 6.307E0 65.51E0
- 7.03E0 70.53E0
- 7.898E0 75.70E0
- 9.470E0 89.57E0
- 9.484E0 91.14E0
- 10.072E0 96.40E0
- 10.163E0 97.19E0
- 11.615E0 114.26E0
- 12.005E0 120.25E0
- 12.478E0 127.08E0
- 12.982E0 133.55E0
- 12.970E0 133.61E0
- 13.926E0 158.67E0
- 14.452E0 172.74E0
- 14.404E0 171.31E0
- 15.190E0 202.14E0
- 15.550E0 220.55E0
- 15.528E0 221.05E0
- 15.499E0 221.39E0
- 16.131E0 250.99E0
- 16.438E0 268.99E0
- 16.387E0 271.80E0
- 16.549E0 271.97E0
- 16.872E0 321.31E0
- 16.830E0 321.69E0
- 16.926E0 330.14E0
- 16.907E0 333.03E0
- 16.966E0 333.47E0
- 17.060E0 340.77E0
- 17.122E0 345.65E0
- 17.311E0 373.11E0
- 17.355E0 373.79E0
- 17.668E0 411.82E0
- 17.767E0 419.51E0
- 17.803E0 421.59E0
- 17.765E0 422.02E0
- 17.768E0 422.47E0
- 17.736E0 422.61E0
- 17.858E0 441.75E0
- 17.877E0 447.41E0
- 17.912E0 448.7E0
- 18.046E0 472.89E0
- 18.085E0 476.69E0
- 18.291E0 522.47E0
- 18.357E0 522.62E0
- 18.426E0 524.43E0
- 18.584E0 546.75E0
- 18.610E0 549.53E0
- 18.870E0 575.29E0
- 18.795E0 576.00E0
- 19.111E0 625.55E0
- .367E0 20.15E0
- .796E0 28.78E0
- 0.892E0 29.57E0
- 1.903E0 37.41E0
- 2.150E0 39.12E0
- 3.697E0 50.24E0
- 5.870E0 61.38E0
- 6.421E0 66.25E0
- 7.422E0 73.42E0
- 9.944E0 95.52E0
- 11.023E0 107.32E0
- 11.87E0 122.04E0
- 12.786E0 134.03E0
- 14.067E0 163.19E0
- 13.974E0 163.48E0
- 14.462E0 175.70E0
- 14.464E0 179.86E0
- 15.381E0 211.27E0
- 15.483E0 217.78E0
- 15.59E0 219.14E0
- 16.075E0 262.52E0
- 16.347E0 268.01E0
- 16.181E0 268.62E0
- 16.915E0 336.25E0
- 17.003E0 337.23E0
- 16.978E0 339.33E0
- 17.756E0 427.38E0
- 17.808E0 428.58E0
- 17.868E0 432.68E0
- 18.481E0 528.99E0
- 18.486E0 531.08E0
- 19.090E0 628.34E0
- 16.062E0 253.24E0
- 16.337E0 273.13E0
- 16.345E0 273.66E0
- 16.388E0 282.10E0
- 17.159E0 346.62E0
- 17.116E0 347.19E0
- 17.164E0 348.78E0
- 17.123E0 351.18E0
- 17.979E0 450.10E0
- 17.974E0 450.35E0
- 18.007E0 451.92E0
- 17.993E0 455.56E0
- 18.523E0 552.22E0
- 18.669E0 553.56E0
- 18.617E0 555.74E0
- 19.371E0 652.59E0
- 19.330E0 656.20E0
- 0.080E0 14.13E0
- 0.248E0 20.41E0
- 1.089E0 31.30E0
- 1.418E0 33.84E0
- 2.278E0 39.70E0
- 3.624E0 48.83E0
- 4.574E0 54.50E0
- 5.556E0 60.41E0
- 7.267E0 72.77E0
- 7.695E0 75.25E0
- 9.136E0 86.84E0
- 9.959E0 94.88E0
- 9.957E0 96.40E0
- 11.600E0 117.37E0
- 13.138E0 139.08E0
- 13.564E0 147.73E0
- 13.871E0 158.63E0
- 13.994E0 161.84E0
- 14.947E0 192.11E0
- 15.473E0 206.76E0
- 15.379E0 209.07E0
- 15.455E0 213.32E0
- 15.908E0 226.44E0
- 16.114E0 237.12E0
- 17.071E0 330.90E0
- 17.135E0 358.72E0
- 17.282E0 370.77E0
- 17.368E0 372.72E0
- 17.483E0 396.24E0
- 17.764E0 416.59E0
- 18.185E0 484.02E0
- 18.271E0 495.47E0
- 18.236E0 514.78E0
- 18.237E0 515.65E0
- 18.523E0 519.47E0
- 18.627E0 544.47E0
- 18.665E0 560.11E0
- 19.086E0 620.77E0
- 0.214E0 18.97E0
- 0.943E0 28.93E0
- 1.429E0 33.91E0
- 2.241E0 40.03E0
- 2.951E0 44.66E0
- 3.782E0 49.87E0
- 4.757E0 55.16E0
- 5.602E0 60.90E0
- 7.169E0 72.08E0
- 8.920E0 85.15E0
- 10.055E0 97.06E0
- 12.035E0 119.63E0
- 12.861E0 133.27E0
- 13.436E0 143.84E0
- 14.167E0 161.91E0
- 14.755E0 180.67E0
- 15.168E0 198.44E0
- 15.651E0 226.86E0
- 15.746E0 229.65E0
- 16.216E0 258.27E0
- 16.445E0 273.77E0
- 16.965E0 339.15E0
- 17.121E0 350.13E0
- 17.206E0 362.75E0
- 17.250E0 371.03E0
- 17.339E0 393.32E0
- 17.793E0 448.53E0
- 18.123E0 473.78E0
- 18.49E0 511.12E0
- 18.566E0 524.70E0
- 18.645E0 548.75E0
- 18.706E0 551.64E0
- 18.924E0 574.02E0
- 19.1E0 623.86E0
- 0.375E0 21.46E0
- 0.471E0 24.33E0
- 1.504E0 33.43E0
- 2.204E0 39.22E0
- 2.813E0 44.18E0
- 4.765E0 55.02E0
- 9.835E0 94.33E0
- 10.040E0 96.44E0
- 11.946E0 118.82E0
- 12.596E0 128.48E0
- 13.303E0 141.94E0
- 13.922E0 156.92E0
- 14.440E0 171.65E0
- 14.951E0 190.00E0
- 15.627E0 223.26E0
- 15.639E0 223.88E0
- 15.814E0 231.50E0
- 16.315E0 265.05E0
- 16.334E0 269.44E0
- 16.430E0 271.78E0
- 16.423E0 273.46E0
- 17.024E0 334.61E0
- 17.009E0 339.79E0
- 17.165E0 349.52E0
- 17.134E0 358.18E0
- 17.349E0 377.98E0
- 17.576E0 394.77E0
- 17.848E0 429.66E0
- 18.090E0 468.22E0
- 18.276E0 487.27E0
- 18.404E0 519.54E0
- 18.519E0 523.03E0
- 19.133E0 612.99E0
- 19.074E0 638.59E0
- 19.239E0 641.36E0
- 19.280E0 622.05E0
- 19.101E0 631.50E0
- 19.398E0 663.97E0
- 19.252E0 646.9E0
- 19.89E0 748.29E0
- 20.007E0 749.21E0
- 19.929E0 750.14E0
- 19.268E0 647.04E0
- 19.324E0 646.89E0
- 20.049E0 746.9E0
- 20.107E0 748.43E0
- 20.062E0 747.35E0
- 20.065E0 749.27E0
- 19.286E0 647.61E0
- 19.972E0 747.78E0
- 20.088E0 750.51E0
- 20.743E0 851.37E0
- 20.83E0 845.97E0
- 20.935E0 847.54E0
- 21.035E0 849.93E0
- 20.93E0 851.61E0
- 21.074E0 849.75E0
- 21.085E0 850.98E0
- 20.935E0 848.23E0
+NIST/ITL StRD
+Dataset Name: Hahn1 (Hahn1.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 47)
+ Certified Values (lines 41 to 52)
+ Data (lines 61 to 296)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are the result of a NIST study involving
+ the thermal expansion of copper. The response
+ variable is the coefficient of thermal expansion, and
+ the predictor variable is temperature in degrees
+ kelvin.
+
+
+Reference: Hahn, T., NIST (197?).
+ Copper Thermal Expansion Study.
+
+
+
+
+
+Data: 1 Response (y = coefficient of thermal expansion)
+ 1 Predictor (x = temperature, degrees kelvin)
+ 236 Observations
+ Average Level of Difficulty
+ Observed Data
+
+Model: Rational Class (cubic/cubic)
+ 7 Parameters (b1 to b7)
+
+ y = (b1+b2*x+b3*x**2+b4*x**3) /
+ (1+b5*x+b6*x**2+b7*x**3) + e
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 10 1 1.0776351733E+00 1.7070154742E-01
+ b2 = -1 -0.1 -1.2269296921E-01 1.2000289189E-02
+ b3 = 0.05 0.005 4.0863750610E-03 2.2508314937E-04
+ b4 = -0.00001 -0.000001 -1.4262662514E-06 2.7578037666E-07
+ b5 = -0.05 -0.005 -5.7609940901E-03 2.4712888219E-04
+ b6 = 0.001 0.0001 2.4053735503E-04 1.0449373768E-05
+ b7 = -0.000001 -0.0000001 -1.2314450199E-07 1.3027335327E-08
+
+Residual Sum of Squares: 1.5324382854E+00
+Residual Standard Deviation: 8.1803852243E-02
+Degrees of Freedom: 229
+Number of Observations: 236
+
+
+
+
+
+
+
+Data: y x
+ .591E0 24.41E0
+ 1.547E0 34.82E0
+ 2.902E0 44.09E0
+ 2.894E0 45.07E0
+ 4.703E0 54.98E0
+ 6.307E0 65.51E0
+ 7.03E0 70.53E0
+ 7.898E0 75.70E0
+ 9.470E0 89.57E0
+ 9.484E0 91.14E0
+ 10.072E0 96.40E0
+ 10.163E0 97.19E0
+ 11.615E0 114.26E0
+ 12.005E0 120.25E0
+ 12.478E0 127.08E0
+ 12.982E0 133.55E0
+ 12.970E0 133.61E0
+ 13.926E0 158.67E0
+ 14.452E0 172.74E0
+ 14.404E0 171.31E0
+ 15.190E0 202.14E0
+ 15.550E0 220.55E0
+ 15.528E0 221.05E0
+ 15.499E0 221.39E0
+ 16.131E0 250.99E0
+ 16.438E0 268.99E0
+ 16.387E0 271.80E0
+ 16.549E0 271.97E0
+ 16.872E0 321.31E0
+ 16.830E0 321.69E0
+ 16.926E0 330.14E0
+ 16.907E0 333.03E0
+ 16.966E0 333.47E0
+ 17.060E0 340.77E0
+ 17.122E0 345.65E0
+ 17.311E0 373.11E0
+ 17.355E0 373.79E0
+ 17.668E0 411.82E0
+ 17.767E0 419.51E0
+ 17.803E0 421.59E0
+ 17.765E0 422.02E0
+ 17.768E0 422.47E0
+ 17.736E0 422.61E0
+ 17.858E0 441.75E0
+ 17.877E0 447.41E0
+ 17.912E0 448.7E0
+ 18.046E0 472.89E0
+ 18.085E0 476.69E0
+ 18.291E0 522.47E0
+ 18.357E0 522.62E0
+ 18.426E0 524.43E0
+ 18.584E0 546.75E0
+ 18.610E0 549.53E0
+ 18.870E0 575.29E0
+ 18.795E0 576.00E0
+ 19.111E0 625.55E0
+ .367E0 20.15E0
+ .796E0 28.78E0
+ 0.892E0 29.57E0
+ 1.903E0 37.41E0
+ 2.150E0 39.12E0
+ 3.697E0 50.24E0
+ 5.870E0 61.38E0
+ 6.421E0 66.25E0
+ 7.422E0 73.42E0
+ 9.944E0 95.52E0
+ 11.023E0 107.32E0
+ 11.87E0 122.04E0
+ 12.786E0 134.03E0
+ 14.067E0 163.19E0
+ 13.974E0 163.48E0
+ 14.462E0 175.70E0
+ 14.464E0 179.86E0
+ 15.381E0 211.27E0
+ 15.483E0 217.78E0
+ 15.59E0 219.14E0
+ 16.075E0 262.52E0
+ 16.347E0 268.01E0
+ 16.181E0 268.62E0
+ 16.915E0 336.25E0
+ 17.003E0 337.23E0
+ 16.978E0 339.33E0
+ 17.756E0 427.38E0
+ 17.808E0 428.58E0
+ 17.868E0 432.68E0
+ 18.481E0 528.99E0
+ 18.486E0 531.08E0
+ 19.090E0 628.34E0
+ 16.062E0 253.24E0
+ 16.337E0 273.13E0
+ 16.345E0 273.66E0
+ 16.388E0 282.10E0
+ 17.159E0 346.62E0
+ 17.116E0 347.19E0
+ 17.164E0 348.78E0
+ 17.123E0 351.18E0
+ 17.979E0 450.10E0
+ 17.974E0 450.35E0
+ 18.007E0 451.92E0
+ 17.993E0 455.56E0
+ 18.523E0 552.22E0
+ 18.669E0 553.56E0
+ 18.617E0 555.74E0
+ 19.371E0 652.59E0
+ 19.330E0 656.20E0
+ 0.080E0 14.13E0
+ 0.248E0 20.41E0
+ 1.089E0 31.30E0
+ 1.418E0 33.84E0
+ 2.278E0 39.70E0
+ 3.624E0 48.83E0
+ 4.574E0 54.50E0
+ 5.556E0 60.41E0
+ 7.267E0 72.77E0
+ 7.695E0 75.25E0
+ 9.136E0 86.84E0
+ 9.959E0 94.88E0
+ 9.957E0 96.40E0
+ 11.600E0 117.37E0
+ 13.138E0 139.08E0
+ 13.564E0 147.73E0
+ 13.871E0 158.63E0
+ 13.994E0 161.84E0
+ 14.947E0 192.11E0
+ 15.473E0 206.76E0
+ 15.379E0 209.07E0
+ 15.455E0 213.32E0
+ 15.908E0 226.44E0
+ 16.114E0 237.12E0
+ 17.071E0 330.90E0
+ 17.135E0 358.72E0
+ 17.282E0 370.77E0
+ 17.368E0 372.72E0
+ 17.483E0 396.24E0
+ 17.764E0 416.59E0
+ 18.185E0 484.02E0
+ 18.271E0 495.47E0
+ 18.236E0 514.78E0
+ 18.237E0 515.65E0
+ 18.523E0 519.47E0
+ 18.627E0 544.47E0
+ 18.665E0 560.11E0
+ 19.086E0 620.77E0
+ 0.214E0 18.97E0
+ 0.943E0 28.93E0
+ 1.429E0 33.91E0
+ 2.241E0 40.03E0
+ 2.951E0 44.66E0
+ 3.782E0 49.87E0
+ 4.757E0 55.16E0
+ 5.602E0 60.90E0
+ 7.169E0 72.08E0
+ 8.920E0 85.15E0
+ 10.055E0 97.06E0
+ 12.035E0 119.63E0
+ 12.861E0 133.27E0
+ 13.436E0 143.84E0
+ 14.167E0 161.91E0
+ 14.755E0 180.67E0
+ 15.168E0 198.44E0
+ 15.651E0 226.86E0
+ 15.746E0 229.65E0
+ 16.216E0 258.27E0
+ 16.445E0 273.77E0
+ 16.965E0 339.15E0
+ 17.121E0 350.13E0
+ 17.206E0 362.75E0
+ 17.250E0 371.03E0
+ 17.339E0 393.32E0
+ 17.793E0 448.53E0
+ 18.123E0 473.78E0
+ 18.49E0 511.12E0
+ 18.566E0 524.70E0
+ 18.645E0 548.75E0
+ 18.706E0 551.64E0
+ 18.924E0 574.02E0
+ 19.1E0 623.86E0
+ 0.375E0 21.46E0
+ 0.471E0 24.33E0
+ 1.504E0 33.43E0
+ 2.204E0 39.22E0
+ 2.813E0 44.18E0
+ 4.765E0 55.02E0
+ 9.835E0 94.33E0
+ 10.040E0 96.44E0
+ 11.946E0 118.82E0
+ 12.596E0 128.48E0
+ 13.303E0 141.94E0
+ 13.922E0 156.92E0
+ 14.440E0 171.65E0
+ 14.951E0 190.00E0
+ 15.627E0 223.26E0
+ 15.639E0 223.88E0
+ 15.814E0 231.50E0
+ 16.315E0 265.05E0
+ 16.334E0 269.44E0
+ 16.430E0 271.78E0
+ 16.423E0 273.46E0
+ 17.024E0 334.61E0
+ 17.009E0 339.79E0
+ 17.165E0 349.52E0
+ 17.134E0 358.18E0
+ 17.349E0 377.98E0
+ 17.576E0 394.77E0
+ 17.848E0 429.66E0
+ 18.090E0 468.22E0
+ 18.276E0 487.27E0
+ 18.404E0 519.54E0
+ 18.519E0 523.03E0
+ 19.133E0 612.99E0
+ 19.074E0 638.59E0
+ 19.239E0 641.36E0
+ 19.280E0 622.05E0
+ 19.101E0 631.50E0
+ 19.398E0 663.97E0
+ 19.252E0 646.9E0
+ 19.89E0 748.29E0
+ 20.007E0 749.21E0
+ 19.929E0 750.14E0
+ 19.268E0 647.04E0
+ 19.324E0 646.89E0
+ 20.049E0 746.9E0
+ 20.107E0 748.43E0
+ 20.062E0 747.35E0
+ 20.065E0 749.27E0
+ 19.286E0 647.61E0
+ 19.972E0 747.78E0
+ 20.088E0 750.51E0
+ 20.743E0 851.37E0
+ 20.83E0 845.97E0
+ 20.935E0 847.54E0
+ 21.035E0 849.93E0
+ 20.93E0 851.61E0
+ 21.074E0 849.75E0
+ 21.085E0 850.98E0
+ 20.935E0 848.23E0
diff --git a/NIST_STRD/Kirby2.dat b/NIST_STRD/Kirby2.dat
index 04df176..75cd80f 100644
--- a/NIST_STRD/Kirby2.dat
+++ b/NIST_STRD/Kirby2.dat
@@ -1,211 +1,211 @@
-NIST/ITL StRD
-Dataset Name: Kirby2 (Kirby2.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 45)
- Certified Values (lines 41 to 50)
- Data (lines 61 to 211)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- scanning electron microscope line with standards.
-
-
-Reference: Kirby, R., NIST (197?).
- Scanning electron microscope line width standards.
-
-
-
-
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 151 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Rational Class (quadratic/quadratic)
- 5 Parameters (b1 to b5)
-
- y = (b1 + b2*x + b3*x**2) /
- (1 + b4*x + b5*x**2) + e
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 2 1.5 1.6745063063E+00 8.7989634338E-02
- b2 = -0.1 -0.15 -1.3927397867E-01 4.1182041386E-03
- b3 = 0.003 0.0025 2.5961181191E-03 4.1856520458E-05
- b4 = -0.001 -0.0015 -1.7241811870E-03 5.8931897355E-05
- b5 = 0.00001 0.00002 2.1664802578E-05 2.0129761919E-07
-
-Residual Sum of Squares: 3.9050739624E+00
-Residual Standard Deviation: 1.6354535131E-01
-Degrees of Freedom: 146
-Number of Observations: 151
-
-
-
-
-
-
-
-
-
-Data: y x
- 0.0082E0 9.65E0
- 0.0112E0 10.74E0
- 0.0149E0 11.81E0
- 0.0198E0 12.88E0
- 0.0248E0 14.06E0
- 0.0324E0 15.28E0
- 0.0420E0 16.63E0
- 0.0549E0 18.19E0
- 0.0719E0 19.88E0
- 0.0963E0 21.84E0
- 0.1291E0 24.00E0
- 0.1710E0 26.25E0
- 0.2314E0 28.86E0
- 0.3227E0 31.85E0
- 0.4809E0 35.79E0
- 0.7084E0 40.18E0
- 1.0220E0 44.74E0
- 1.4580E0 49.53E0
- 1.9520E0 53.94E0
- 2.5410E0 58.29E0
- 3.2230E0 62.63E0
- 3.9990E0 67.03E0
- 4.8520E0 71.25E0
- 5.7320E0 75.22E0
- 6.7270E0 79.33E0
- 7.8350E0 83.56E0
- 9.0250E0 87.75E0
- 10.2670E0 91.93E0
- 11.5780E0 96.10E0
- 12.9440E0 100.28E0
- 14.3770E0 104.46E0
- 15.8560E0 108.66E0
- 17.3310E0 112.71E0
- 18.8850E0 116.88E0
- 20.5750E0 121.33E0
- 22.3200E0 125.79E0
- 22.3030E0 125.79E0
- 23.4600E0 128.74E0
- 24.0600E0 130.27E0
- 25.2720E0 133.33E0
- 25.8530E0 134.79E0
- 27.1100E0 137.93E0
- 27.6580E0 139.33E0
- 28.9240E0 142.46E0
- 29.5110E0 143.90E0
- 30.7100E0 146.91E0
- 31.3500E0 148.51E0
- 32.5200E0 151.41E0
- 33.2300E0 153.17E0
- 34.3300E0 155.97E0
- 35.0600E0 157.76E0
- 36.1700E0 160.56E0
- 36.8400E0 162.30E0
- 38.0100E0 165.21E0
- 38.6700E0 166.90E0
- 39.8700E0 169.92E0
- 40.0300E0 170.32E0
- 40.5000E0 171.54E0
- 41.3700E0 173.79E0
- 41.6700E0 174.57E0
- 42.3100E0 176.25E0
- 42.7300E0 177.34E0
- 43.4600E0 179.19E0
- 44.1400E0 181.02E0
- 44.5500E0 182.08E0
- 45.2200E0 183.88E0
- 45.9200E0 185.75E0
- 46.3000E0 186.80E0
- 47.0000E0 188.63E0
- 47.6800E0 190.45E0
- 48.0600E0 191.48E0
- 48.7400E0 193.35E0
- 49.4100E0 195.22E0
- 49.7600E0 196.23E0
- 50.4300E0 198.05E0
- 51.1100E0 199.97E0
- 51.5000E0 201.06E0
- 52.1200E0 202.83E0
- 52.7600E0 204.69E0
- 53.1800E0 205.86E0
- 53.7800E0 207.58E0
- 54.4600E0 209.50E0
- 54.8300E0 210.65E0
- 55.4000E0 212.33E0
- 56.4300E0 215.43E0
- 57.0300E0 217.16E0
- 58.0000E0 220.21E0
- 58.6100E0 221.98E0
- 59.5800E0 225.06E0
- 60.1100E0 226.79E0
- 61.1000E0 229.92E0
- 61.6500E0 231.69E0
- 62.5900E0 234.77E0
- 63.1200E0 236.60E0
- 64.0300E0 239.63E0
- 64.6200E0 241.50E0
- 65.4900E0 244.48E0
- 66.0300E0 246.40E0
- 66.8900E0 249.35E0
- 67.4200E0 251.32E0
- 68.2300E0 254.22E0
- 68.7700E0 256.24E0
- 69.5900E0 259.11E0
- 70.1100E0 261.18E0
- 70.8600E0 264.02E0
- 71.4300E0 266.13E0
- 72.1600E0 268.94E0
- 72.7000E0 271.09E0
- 73.4000E0 273.87E0
- 73.9300E0 276.08E0
- 74.6000E0 278.83E0
- 75.1600E0 281.08E0
- 75.8200E0 283.81E0
- 76.3400E0 286.11E0
- 76.9800E0 288.81E0
- 77.4800E0 291.08E0
- 78.0800E0 293.75E0
- 78.6000E0 295.99E0
- 79.1700E0 298.64E0
- 79.6200E0 300.84E0
- 79.8800E0 302.02E0
- 80.1900E0 303.48E0
- 80.6600E0 305.65E0
- 81.2200E0 308.27E0
- 81.6600E0 310.41E0
- 82.1600E0 313.01E0
- 82.5900E0 315.12E0
- 83.1400E0 317.71E0
- 83.5000E0 319.79E0
- 84.0000E0 322.36E0
- 84.4000E0 324.42E0
- 84.8900E0 326.98E0
- 85.2600E0 329.01E0
- 85.7400E0 331.56E0
- 86.0700E0 333.56E0
- 86.5400E0 336.10E0
- 86.8900E0 338.08E0
- 87.3200E0 340.60E0
- 87.6500E0 342.57E0
- 88.1000E0 345.08E0
- 88.4300E0 347.02E0
- 88.8300E0 349.52E0
- 89.1200E0 351.44E0
- 89.5400E0 353.93E0
- 89.8500E0 355.83E0
- 90.2500E0 358.32E0
- 90.5500E0 360.20E0
- 90.9300E0 362.67E0
- 91.2000E0 364.53E0
- 91.5500E0 367.00E0
- 92.2000E0 371.30E0
+NIST/ITL StRD
+Dataset Name: Kirby2 (Kirby2.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 45)
+ Certified Values (lines 41 to 50)
+ Data (lines 61 to 211)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are the result of a NIST study involving
+ scanning electron microscope line with standards.
+
+
+Reference: Kirby, R., NIST (197?).
+ Scanning electron microscope line width standards.
+
+
+
+
+
+
+
+
+Data: 1 Response (y)
+ 1 Predictor (x)
+ 151 Observations
+ Average Level of Difficulty
+ Observed Data
+
+Model: Rational Class (quadratic/quadratic)
+ 5 Parameters (b1 to b5)
+
+ y = (b1 + b2*x + b3*x**2) /
+ (1 + b4*x + b5*x**2) + e
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 2 1.5 1.6745063063E+00 8.7989634338E-02
+ b2 = -0.1 -0.15 -1.3927397867E-01 4.1182041386E-03
+ b3 = 0.003 0.0025 2.5961181191E-03 4.1856520458E-05
+ b4 = -0.001 -0.0015 -1.7241811870E-03 5.8931897355E-05
+ b5 = 0.00001 0.00002 2.1664802578E-05 2.0129761919E-07
+
+Residual Sum of Squares: 3.9050739624E+00
+Residual Standard Deviation: 1.6354535131E-01
+Degrees of Freedom: 146
+Number of Observations: 151
+
+
+
+
+
+
+
+
+
+Data: y x
+ 0.0082E0 9.65E0
+ 0.0112E0 10.74E0
+ 0.0149E0 11.81E0
+ 0.0198E0 12.88E0
+ 0.0248E0 14.06E0
+ 0.0324E0 15.28E0
+ 0.0420E0 16.63E0
+ 0.0549E0 18.19E0
+ 0.0719E0 19.88E0
+ 0.0963E0 21.84E0
+ 0.1291E0 24.00E0
+ 0.1710E0 26.25E0
+ 0.2314E0 28.86E0
+ 0.3227E0 31.85E0
+ 0.4809E0 35.79E0
+ 0.7084E0 40.18E0
+ 1.0220E0 44.74E0
+ 1.4580E0 49.53E0
+ 1.9520E0 53.94E0
+ 2.5410E0 58.29E0
+ 3.2230E0 62.63E0
+ 3.9990E0 67.03E0
+ 4.8520E0 71.25E0
+ 5.7320E0 75.22E0
+ 6.7270E0 79.33E0
+ 7.8350E0 83.56E0
+ 9.0250E0 87.75E0
+ 10.2670E0 91.93E0
+ 11.5780E0 96.10E0
+ 12.9440E0 100.28E0
+ 14.3770E0 104.46E0
+ 15.8560E0 108.66E0
+ 17.3310E0 112.71E0
+ 18.8850E0 116.88E0
+ 20.5750E0 121.33E0
+ 22.3200E0 125.79E0
+ 22.3030E0 125.79E0
+ 23.4600E0 128.74E0
+ 24.0600E0 130.27E0
+ 25.2720E0 133.33E0
+ 25.8530E0 134.79E0
+ 27.1100E0 137.93E0
+ 27.6580E0 139.33E0
+ 28.9240E0 142.46E0
+ 29.5110E0 143.90E0
+ 30.7100E0 146.91E0
+ 31.3500E0 148.51E0
+ 32.5200E0 151.41E0
+ 33.2300E0 153.17E0
+ 34.3300E0 155.97E0
+ 35.0600E0 157.76E0
+ 36.1700E0 160.56E0
+ 36.8400E0 162.30E0
+ 38.0100E0 165.21E0
+ 38.6700E0 166.90E0
+ 39.8700E0 169.92E0
+ 40.0300E0 170.32E0
+ 40.5000E0 171.54E0
+ 41.3700E0 173.79E0
+ 41.6700E0 174.57E0
+ 42.3100E0 176.25E0
+ 42.7300E0 177.34E0
+ 43.4600E0 179.19E0
+ 44.1400E0 181.02E0
+ 44.5500E0 182.08E0
+ 45.2200E0 183.88E0
+ 45.9200E0 185.75E0
+ 46.3000E0 186.80E0
+ 47.0000E0 188.63E0
+ 47.6800E0 190.45E0
+ 48.0600E0 191.48E0
+ 48.7400E0 193.35E0
+ 49.4100E0 195.22E0
+ 49.7600E0 196.23E0
+ 50.4300E0 198.05E0
+ 51.1100E0 199.97E0
+ 51.5000E0 201.06E0
+ 52.1200E0 202.83E0
+ 52.7600E0 204.69E0
+ 53.1800E0 205.86E0
+ 53.7800E0 207.58E0
+ 54.4600E0 209.50E0
+ 54.8300E0 210.65E0
+ 55.4000E0 212.33E0
+ 56.4300E0 215.43E0
+ 57.0300E0 217.16E0
+ 58.0000E0 220.21E0
+ 58.6100E0 221.98E0
+ 59.5800E0 225.06E0
+ 60.1100E0 226.79E0
+ 61.1000E0 229.92E0
+ 61.6500E0 231.69E0
+ 62.5900E0 234.77E0
+ 63.1200E0 236.60E0
+ 64.0300E0 239.63E0
+ 64.6200E0 241.50E0
+ 65.4900E0 244.48E0
+ 66.0300E0 246.40E0
+ 66.8900E0 249.35E0
+ 67.4200E0 251.32E0
+ 68.2300E0 254.22E0
+ 68.7700E0 256.24E0
+ 69.5900E0 259.11E0
+ 70.1100E0 261.18E0
+ 70.8600E0 264.02E0
+ 71.4300E0 266.13E0
+ 72.1600E0 268.94E0
+ 72.7000E0 271.09E0
+ 73.4000E0 273.87E0
+ 73.9300E0 276.08E0
+ 74.6000E0 278.83E0
+ 75.1600E0 281.08E0
+ 75.8200E0 283.81E0
+ 76.3400E0 286.11E0
+ 76.9800E0 288.81E0
+ 77.4800E0 291.08E0
+ 78.0800E0 293.75E0
+ 78.6000E0 295.99E0
+ 79.1700E0 298.64E0
+ 79.6200E0 300.84E0
+ 79.8800E0 302.02E0
+ 80.1900E0 303.48E0
+ 80.6600E0 305.65E0
+ 81.2200E0 308.27E0
+ 81.6600E0 310.41E0
+ 82.1600E0 313.01E0
+ 82.5900E0 315.12E0
+ 83.1400E0 317.71E0
+ 83.5000E0 319.79E0
+ 84.0000E0 322.36E0
+ 84.4000E0 324.42E0
+ 84.8900E0 326.98E0
+ 85.2600E0 329.01E0
+ 85.7400E0 331.56E0
+ 86.0700E0 333.56E0
+ 86.5400E0 336.10E0
+ 86.8900E0 338.08E0
+ 87.3200E0 340.60E0
+ 87.6500E0 342.57E0
+ 88.1000E0 345.08E0
+ 88.4300E0 347.02E0
+ 88.8300E0 349.52E0
+ 89.1200E0 351.44E0
+ 89.5400E0 353.93E0
+ 89.8500E0 355.83E0
+ 90.2500E0 358.32E0
+ 90.5500E0 360.20E0
+ 90.9300E0 362.67E0
+ 91.2000E0 364.53E0
+ 91.5500E0 367.00E0
+ 92.2000E0 371.30E0
diff --git a/NIST_STRD/Lanczos1.dat b/NIST_STRD/Lanczos1.dat
index 8107320..d23d5e4 100644
--- a/NIST_STRD/Lanczos1.dat
+++ b/NIST_STRD/Lanczos1.dat
@@ -1,84 +1,84 @@
-NIST/ITL StRD
-Dataset Name: Lanczos1 (Lanczos1.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 46)
- Certified Values (lines 41 to 51)
- Data (lines 61 to 84)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are taken from an example discussed in
- Lanczos (1956). The data were generated to 14-digits
- of accuracy using
- f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x)
- + 1.5576*exp(-5*x).
-
-
-Reference: Lanczos, C. (1956).
- Applied Analysis.
- Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 24 Observations
- Average Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 6 Parameters (b1 to b6)
-
- y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1.2 0.5 9.5100000027E-02 5.3347304234E-11
- b2 = 0.3 0.7 1.0000000001E+00 2.7473038179E-10
- b3 = 5.6 3.6 8.6070000013E-01 1.3576062225E-10
- b4 = 5.5 4.2 3.0000000002E+00 3.3308253069E-10
- b5 = 6.5 4 1.5575999998E+00 1.8815731448E-10
- b6 = 7.6 6.3 5.0000000001E+00 1.1057500538E-10
-
-Residual Sum of Squares: 1.4307867721E-25
-Residual Standard Deviation: 8.9156129349E-14
-Degrees of Freedom: 18
-Number of Observations: 24
-
-
-
-
-
-
-
-
-Data: y x
- 2.513400000000E+00 0.000000000000E+00
- 2.044333373291E+00 5.000000000000E-02
- 1.668404436564E+00 1.000000000000E-01
- 1.366418021208E+00 1.500000000000E-01
- 1.123232487372E+00 2.000000000000E-01
- 9.268897180037E-01 2.500000000000E-01
- 7.679338563728E-01 3.000000000000E-01
- 6.388775523106E-01 3.500000000000E-01
- 5.337835317402E-01 4.000000000000E-01
- 4.479363617347E-01 4.500000000000E-01
- 3.775847884350E-01 5.000000000000E-01
- 3.197393199326E-01 5.500000000000E-01
- 2.720130773746E-01 6.000000000000E-01
- 2.324965529032E-01 6.500000000000E-01
- 1.996589546065E-01 7.000000000000E-01
- 1.722704126914E-01 7.500000000000E-01
- 1.493405660168E-01 8.000000000000E-01
- 1.300700206922E-01 8.500000000000E-01
- 1.138119324644E-01 9.000000000000E-01
- 1.000415587559E-01 9.500000000000E-01
- 8.833209084540E-02 1.000000000000E+00
- 7.833544019350E-02 1.050000000000E+00
- 6.976693743449E-02 1.100000000000E+00
- 6.239312536719E-02 1.150000000000E+00
+NIST/ITL StRD
+Dataset Name: Lanczos1 (Lanczos1.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 46)
+ Certified Values (lines 41 to 51)
+ Data (lines 61 to 84)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are taken from an example discussed in
+ Lanczos (1956). The data were generated to 14-digits
+ of accuracy using
+ f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x)
+ + 1.5576*exp(-5*x).
+
+
+Reference: Lanczos, C. (1956).
+ Applied Analysis.
+ Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
+
+
+
+
+Data: 1 Response (y)
+ 1 Predictor (x)
+ 24 Observations
+ Average Level of Difficulty
+ Generated Data
+
+Model: Exponential Class
+ 6 Parameters (b1 to b6)
+
+ y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 1.2 0.5 9.5100000027E-02 5.3347304234E-11
+ b2 = 0.3 0.7 1.0000000001E+00 2.7473038179E-10
+ b3 = 5.6 3.6 8.6070000013E-01 1.3576062225E-10
+ b4 = 5.5 4.2 3.0000000002E+00 3.3308253069E-10
+ b5 = 6.5 4 1.5575999998E+00 1.8815731448E-10
+ b6 = 7.6 6.3 5.0000000001E+00 1.1057500538E-10
+
+Residual Sum of Squares: 1.4307867721E-25
+Residual Standard Deviation: 8.9156129349E-14
+Degrees of Freedom: 18
+Number of Observations: 24
+
+
+
+
+
+
+
+
+Data: y x
+ 2.513400000000E+00 0.000000000000E+00
+ 2.044333373291E+00 5.000000000000E-02
+ 1.668404436564E+00 1.000000000000E-01
+ 1.366418021208E+00 1.500000000000E-01
+ 1.123232487372E+00 2.000000000000E-01
+ 9.268897180037E-01 2.500000000000E-01
+ 7.679338563728E-01 3.000000000000E-01
+ 6.388775523106E-01 3.500000000000E-01
+ 5.337835317402E-01 4.000000000000E-01
+ 4.479363617347E-01 4.500000000000E-01
+ 3.775847884350E-01 5.000000000000E-01
+ 3.197393199326E-01 5.500000000000E-01
+ 2.720130773746E-01 6.000000000000E-01
+ 2.324965529032E-01 6.500000000000E-01
+ 1.996589546065E-01 7.000000000000E-01
+ 1.722704126914E-01 7.500000000000E-01
+ 1.493405660168E-01 8.000000000000E-01
+ 1.300700206922E-01 8.500000000000E-01
+ 1.138119324644E-01 9.000000000000E-01
+ 1.000415587559E-01 9.500000000000E-01
+ 8.833209084540E-02 1.000000000000E+00
+ 7.833544019350E-02 1.050000000000E+00
+ 6.976693743449E-02 1.100000000000E+00
+ 6.239312536719E-02 1.150000000000E+00
diff --git a/NIST_STRD/Lanczos2.dat b/NIST_STRD/Lanczos2.dat
index fc98e69..f9f2b4b 100644
--- a/NIST_STRD/Lanczos2.dat
+++ b/NIST_STRD/Lanczos2.dat
@@ -1,84 +1,84 @@
-NIST/ITL StRD
-Dataset Name: Lanczos2 (Lanczos2.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 46)
- Certified Values (lines 41 to 51)
- Data (lines 61 to 84)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are taken from an example discussed in
- Lanczos (1956). The data were generated to 6-digits
- of accuracy using
- f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x)
- + 1.5576*exp(-5*x).
-
-
-Reference: Lanczos, C. (1956).
- Applied Analysis.
- Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 24 Observations
- Average Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 6 Parameters (b1 to b6)
-
- y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1.2 0.5 9.6251029939E-02 6.6770575477E-04
- b2 = 0.3 0.7 1.0057332849E+00 3.3989646176E-03
- b3 = 5.6 3.6 8.6424689056E-01 1.7185846685E-03
- b4 = 5.5 4.2 3.0078283915E+00 4.1707005856E-03
- b5 = 6.5 4 1.5529016879E+00 2.3744381417E-03
- b6 = 7.6 6.3 5.0028798100E+00 1.3958787284E-03
-
-Residual Sum of Squares: 2.2299428125E-11
-Residual Standard Deviation: 1.1130395851E-06
-Degrees of Freedom: 18
-Number of Observations: 24
-
-
-
-
-
-
-
-
-Data: y x
- 2.51340E+00 0.00000E+00
- 2.04433E+00 5.00000E-02
- 1.66840E+00 1.00000E-01
- 1.36642E+00 1.50000E-01
- 1.12323E+00 2.00000E-01
- 9.26890E-01 2.50000E-01
- 7.67934E-01 3.00000E-01
- 6.38878E-01 3.50000E-01
- 5.33784E-01 4.00000E-01
- 4.47936E-01 4.50000E-01
- 3.77585E-01 5.00000E-01
- 3.19739E-01 5.50000E-01
- 2.72013E-01 6.00000E-01
- 2.32497E-01 6.50000E-01
- 1.99659E-01 7.00000E-01
- 1.72270E-01 7.50000E-01
- 1.49341E-01 8.00000E-01
- 1.30070E-01 8.50000E-01
- 1.13812E-01 9.00000E-01
- 1.00042E-01 9.50000E-01
- 8.83321E-02 1.00000E+00
- 7.83354E-02 1.05000E+00
- 6.97669E-02 1.10000E+00
- 6.23931E-02 1.15000E+00
+NIST/ITL StRD
+Dataset Name: Lanczos2 (Lanczos2.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 46)
+ Certified Values (lines 41 to 51)
+ Data (lines 61 to 84)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are taken from an example discussed in
+ Lanczos (1956). The data were generated to 6-digits
+ of accuracy using
+ f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x)
+ + 1.5576*exp(-5*x).
+
+
+Reference: Lanczos, C. (1956).
+ Applied Analysis.
+ Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
+
+
+
+
+Data: 1 Response (y)
+ 1 Predictor (x)
+ 24 Observations
+ Average Level of Difficulty
+ Generated Data
+
+Model: Exponential Class
+ 6 Parameters (b1 to b6)
+
+ y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 1.2 0.5 9.6251029939E-02 6.6770575477E-04
+ b2 = 0.3 0.7 1.0057332849E+00 3.3989646176E-03
+ b3 = 5.6 3.6 8.6424689056E-01 1.7185846685E-03
+ b4 = 5.5 4.2 3.0078283915E+00 4.1707005856E-03
+ b5 = 6.5 4 1.5529016879E+00 2.3744381417E-03
+ b6 = 7.6 6.3 5.0028798100E+00 1.3958787284E-03
+
+Residual Sum of Squares: 2.2299428125E-11
+Residual Standard Deviation: 1.1130395851E-06
+Degrees of Freedom: 18
+Number of Observations: 24
+
+
+
+
+
+
+
+
+Data: y x
+ 2.51340E+00 0.00000E+00
+ 2.04433E+00 5.00000E-02
+ 1.66840E+00 1.00000E-01
+ 1.36642E+00 1.50000E-01
+ 1.12323E+00 2.00000E-01
+ 9.26890E-01 2.50000E-01
+ 7.67934E-01 3.00000E-01
+ 6.38878E-01 3.50000E-01
+ 5.33784E-01 4.00000E-01
+ 4.47936E-01 4.50000E-01
+ 3.77585E-01 5.00000E-01
+ 3.19739E-01 5.50000E-01
+ 2.72013E-01 6.00000E-01
+ 2.32497E-01 6.50000E-01
+ 1.99659E-01 7.00000E-01
+ 1.72270E-01 7.50000E-01
+ 1.49341E-01 8.00000E-01
+ 1.30070E-01 8.50000E-01
+ 1.13812E-01 9.00000E-01
+ 1.00042E-01 9.50000E-01
+ 8.83321E-02 1.00000E+00
+ 7.83354E-02 1.05000E+00
+ 6.97669E-02 1.10000E+00
+ 6.23931E-02 1.15000E+00
diff --git a/NIST_STRD/Lanczos3.dat b/NIST_STRD/Lanczos3.dat
index d930d65..67c1512 100644
--- a/NIST_STRD/Lanczos3.dat
+++ b/NIST_STRD/Lanczos3.dat
@@ -1,84 +1,84 @@
-NIST/ITL StRD
-Dataset Name: Lanczos3 (Lanczos3.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 46)
- Certified Values (lines 41 to 51)
- Data (lines 61 to 84)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are taken from an example discussed in
- Lanczos (1956). The data were generated to 5-digits
- of accuracy using
- f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x)
- + 1.5576*exp(-5*x).
-
-
-Reference: Lanczos, C. (1956).
- Applied Analysis.
- Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 24 Observations
- Lower Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 6 Parameters (b1 to b6)
-
- y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1.2 0.5 8.6816414977E-02 1.7197908859E-02
- b2 = 0.3 0.7 9.5498101505E-01 9.7041624475E-02
- b3 = 5.6 3.6 8.4400777463E-01 4.1488663282E-02
- b4 = 5.5 4.2 2.9515951832E+00 1.0766312506E-01
- b5 = 6.5 4 1.5825685901E+00 5.8371576281E-02
- b6 = 7.6 6.3 4.9863565084E+00 3.4436403035E-02
-
-Residual Sum of Squares: 1.6117193594E-08
-Residual Standard Deviation: 2.9923229172E-05
-Degrees of Freedom: 18
-Number of Observations: 24
-
-
-
-
-
-
-
-
-Data: y x
- 2.5134E+00 0.00000E+00
- 2.0443E+00 5.00000E-02
- 1.6684E+00 1.00000E-01
- 1.3664E+00 1.50000E-01
- 1.1232E+00 2.00000E-01
- 0.9269E+00 2.50000E-01
- 0.7679E+00 3.00000E-01
- 0.6389E+00 3.50000E-01
- 0.5338E+00 4.00000E-01
- 0.4479E+00 4.50000E-01
- 0.3776E+00 5.00000E-01
- 0.3197E+00 5.50000E-01
- 0.2720E+00 6.00000E-01
- 0.2325E+00 6.50000E-01
- 0.1997E+00 7.00000E-01
- 0.1723E+00 7.50000E-01
- 0.1493E+00 8.00000E-01
- 0.1301E+00 8.50000E-01
- 0.1138E+00 9.00000E-01
- 0.1000E+00 9.50000E-01
- 0.0883E+00 1.00000E+00
- 0.0783E+00 1.05000E+00
- 0.0698E+00 1.10000E+00
- 0.0624E+00 1.15000E+00
+NIST/ITL StRD
+Dataset Name: Lanczos3 (Lanczos3.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 46)
+ Certified Values (lines 41 to 51)
+ Data (lines 61 to 84)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are taken from an example discussed in
+ Lanczos (1956). The data were generated to 5-digits
+ of accuracy using
+ f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x)
+ + 1.5576*exp(-5*x).
+
+
+Reference: Lanczos, C. (1956).
+ Applied Analysis.
+ Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
+
+
+
+
+Data: 1 Response (y)
+ 1 Predictor (x)
+ 24 Observations
+ Lower Level of Difficulty
+ Generated Data
+
+Model: Exponential Class
+ 6 Parameters (b1 to b6)
+
+ y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 1.2 0.5 8.6816414977E-02 1.7197908859E-02
+ b2 = 0.3 0.7 9.5498101505E-01 9.7041624475E-02
+ b3 = 5.6 3.6 8.4400777463E-01 4.1488663282E-02
+ b4 = 5.5 4.2 2.9515951832E+00 1.0766312506E-01
+ b5 = 6.5 4 1.5825685901E+00 5.8371576281E-02
+ b6 = 7.6 6.3 4.9863565084E+00 3.4436403035E-02
+
+Residual Sum of Squares: 1.6117193594E-08
+Residual Standard Deviation: 2.9923229172E-05
+Degrees of Freedom: 18
+Number of Observations: 24
+
+
+
+
+
+
+
+
+Data: y x
+ 2.5134E+00 0.00000E+00
+ 2.0443E+00 5.00000E-02
+ 1.6684E+00 1.00000E-01
+ 1.3664E+00 1.50000E-01
+ 1.1232E+00 2.00000E-01
+ 0.9269E+00 2.50000E-01
+ 0.7679E+00 3.00000E-01
+ 0.6389E+00 3.50000E-01
+ 0.5338E+00 4.00000E-01
+ 0.4479E+00 4.50000E-01
+ 0.3776E+00 5.00000E-01
+ 0.3197E+00 5.50000E-01
+ 0.2720E+00 6.00000E-01
+ 0.2325E+00 6.50000E-01
+ 0.1997E+00 7.00000E-01
+ 0.1723E+00 7.50000E-01
+ 0.1493E+00 8.00000E-01
+ 0.1301E+00 8.50000E-01
+ 0.1138E+00 9.00000E-01
+ 0.1000E+00 9.50000E-01
+ 0.0883E+00 1.00000E+00
+ 0.0783E+00 1.05000E+00
+ 0.0698E+00 1.10000E+00
+ 0.0624E+00 1.15000E+00
diff --git a/NIST_STRD/MGH09.dat b/NIST_STRD/MGH09.dat
index 1f19af8..55a2d42 100644
--- a/NIST_STRD/MGH09.dat
+++ b/NIST_STRD/MGH09.dat
@@ -1,71 +1,71 @@
-NIST/ITL StRD
-Dataset Name: MGH09 (MGH09.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 44)
- Certified Values (lines 41 to 49)
- Data (lines 61 to 71)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: This problem was found to be difficult for some very
- good algorithms. There is a local minimum at (+inf,
- -14.07..., -inf, -inf) with final sum of squares
- 0.00102734....
-
- See More, J. J., Garbow, B. S., and Hillstrom, K. E.
- (1981). Testing unconstrained optimization software.
- ACM Transactions on Mathematical Software. 7(1):
- pp. 17-41.
-
-Reference: Kowalik, J.S., and M. R. Osborne, (1978).
- Methods for Unconstrained Optimization Problems.
- New York, NY: Elsevier North-Holland.
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 11 Observations
- Higher Level of Difficulty
- Generated Data
-
-Model: Rational Class (linear/quadratic)
- 4 Parameters (b1 to b4)
-
- y = b1*(x**2+x*b2) / (x**2+x*b3+b4) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 25 0.25 1.9280693458E-01 1.1435312227E-02
- b2 = 39 0.39 1.9128232873E-01 1.9633220911E-01
- b3 = 41.5 0.415 1.2305650693E-01 8.0842031232E-02
- b4 = 39 0.39 1.3606233068E-01 9.0025542308E-02
-
-Residual Sum of Squares: 3.0750560385E-04
-Residual Standard Deviation: 6.6279236551E-03
-Degrees of Freedom: 7
-Number of Observations: 11
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 1.957000E-01 4.000000E+00
- 1.947000E-01 2.000000E+00
- 1.735000E-01 1.000000E+00
- 1.600000E-01 5.000000E-01
- 8.440000E-02 2.500000E-01
- 6.270000E-02 1.670000E-01
- 4.560000E-02 1.250000E-01
- 3.420000E-02 1.000000E-01
- 3.230000E-02 8.330000E-02
- 2.350000E-02 7.140000E-02
- 2.460000E-02 6.250000E-02
+NIST/ITL StRD
+Dataset Name: MGH09 (MGH09.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 44)
+ Certified Values (lines 41 to 49)
+ Data (lines 61 to 71)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: This problem was found to be difficult for some very
+ good algorithms. There is a local minimum at (+inf,
+ -14.07..., -inf, -inf) with final sum of squares
+ 0.00102734....
+
+ See More, J. J., Garbow, B. S., and Hillstrom, K. E.
+ (1981). Testing unconstrained optimization software.
+ ACM Transactions on Mathematical Software. 7(1):
+ pp. 17-41.
+
+Reference: Kowalik, J.S., and M. R. Osborne, (1978).
+ Methods for Unconstrained Optimization Problems.
+ New York, NY: Elsevier North-Holland.
+
+Data: 1 Response (y)
+ 1 Predictor (x)
+ 11 Observations
+ Higher Level of Difficulty
+ Generated Data
+
+Model: Rational Class (linear/quadratic)
+ 4 Parameters (b1 to b4)
+
+ y = b1*(x**2+x*b2) / (x**2+x*b3+b4) + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 25 0.25 1.9280693458E-01 1.1435312227E-02
+ b2 = 39 0.39 1.9128232873E-01 1.9633220911E-01
+ b3 = 41.5 0.415 1.2305650693E-01 8.0842031232E-02
+ b4 = 39 0.39 1.3606233068E-01 9.0025542308E-02
+
+Residual Sum of Squares: 3.0750560385E-04
+Residual Standard Deviation: 6.6279236551E-03
+Degrees of Freedom: 7
+Number of Observations: 11
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 1.957000E-01 4.000000E+00
+ 1.947000E-01 2.000000E+00
+ 1.735000E-01 1.000000E+00
+ 1.600000E-01 5.000000E-01
+ 8.440000E-02 2.500000E-01
+ 6.270000E-02 1.670000E-01
+ 4.560000E-02 1.250000E-01
+ 3.420000E-02 1.000000E-01
+ 3.230000E-02 8.330000E-02
+ 2.350000E-02 7.140000E-02
+ 2.460000E-02 6.250000E-02
diff --git a/NIST_STRD/MGH10.dat b/NIST_STRD/MGH10.dat
index df88ea4..b2ffbec 100644
--- a/NIST_STRD/MGH10.dat
+++ b/NIST_STRD/MGH10.dat
@@ -1,76 +1,76 @@
-NIST/ITL StRD
-Dataset Name: MGH10 (MGH10.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 76)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: This problem was found to be difficult for some very
- good algorithms.
-
- See More, J. J., Garbow, B. S., and Hillstrom, K. E.
- (1981). Testing unconstrained optimization software.
- ACM Transactions on Mathematical Software. 7(1):
- pp. 17-41.
-
-Reference: Meyer, R. R. (1970).
- Theoretical and computational aspects of nonlinear
- regression. In Nonlinear Programming, Rosen,
- Mangasarian and Ritter (Eds).
- New York, NY: Academic Press, pp. 465-486.
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 16 Observations
- Higher Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 3 Parameters (b1 to b3)
-
- y = b1 * exp[b2/(x+b3)] + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 2 0.02 5.6096364710E-03 1.5687892471E-04
- b2 = 400000 4000 6.1813463463E+03 2.3309021107E+01
- b3 = 25000 250 3.4522363462E+02 7.8486103508E-01
-
-Residual Sum of Squares: 8.7945855171E+01
-Residual Standard Deviation: 2.6009740065E+00
-Degrees of Freedom: 13
-Number of Observations: 16
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 3.478000E+04 5.000000E+01
- 2.861000E+04 5.500000E+01
- 2.365000E+04 6.000000E+01
- 1.963000E+04 6.500000E+01
- 1.637000E+04 7.000000E+01
- 1.372000E+04 7.500000E+01
- 1.154000E+04 8.000000E+01
- 9.744000E+03 8.500000E+01
- 8.261000E+03 9.000000E+01
- 7.030000E+03 9.500000E+01
- 6.005000E+03 1.000000E+02
- 5.147000E+03 1.050000E+02
- 4.427000E+03 1.100000E+02
- 3.820000E+03 1.150000E+02
- 3.307000E+03 1.200000E+02
- 2.872000E+03 1.250000E+02
+NIST/ITL StRD
+Dataset Name: MGH10 (MGH10.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 43)
+ Certified Values (lines 41 to 48)
+ Data (lines 61 to 76)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: This problem was found to be difficult for some very
+ good algorithms.
+
+ See More, J. J., Garbow, B. S., and Hillstrom, K. E.
+ (1981). Testing unconstrained optimization software.
+ ACM Transactions on Mathematical Software. 7(1):
+ pp. 17-41.
+
+Reference: Meyer, R. R. (1970).
+ Theoretical and computational aspects of nonlinear
+ regression. In Nonlinear Programming, Rosen,
+ Mangasarian and Ritter (Eds).
+ New York, NY: Academic Press, pp. 465-486.
+
+Data: 1 Response (y)
+ 1 Predictor (x)
+ 16 Observations
+ Higher Level of Difficulty
+ Generated Data
+
+Model: Exponential Class
+ 3 Parameters (b1 to b3)
+
+ y = b1 * exp[b2/(x+b3)] + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 2 0.02 5.6096364710E-03 1.5687892471E-04
+ b2 = 400000 4000 6.1813463463E+03 2.3309021107E+01
+ b3 = 25000 250 3.4522363462E+02 7.8486103508E-01
+
+Residual Sum of Squares: 8.7945855171E+01
+Residual Standard Deviation: 2.6009740065E+00
+Degrees of Freedom: 13
+Number of Observations: 16
+
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 3.478000E+04 5.000000E+01
+ 2.861000E+04 5.500000E+01
+ 2.365000E+04 6.000000E+01
+ 1.963000E+04 6.500000E+01
+ 1.637000E+04 7.000000E+01
+ 1.372000E+04 7.500000E+01
+ 1.154000E+04 8.000000E+01
+ 9.744000E+03 8.500000E+01
+ 8.261000E+03 9.000000E+01
+ 7.030000E+03 9.500000E+01
+ 6.005000E+03 1.000000E+02
+ 5.147000E+03 1.050000E+02
+ 4.427000E+03 1.100000E+02
+ 3.820000E+03 1.150000E+02
+ 3.307000E+03 1.200000E+02
+ 2.872000E+03 1.250000E+02
diff --git a/NIST_STRD/MGH17.dat b/NIST_STRD/MGH17.dat
index 3b3b7e8..584f73c 100644
--- a/NIST_STRD/MGH17.dat
+++ b/NIST_STRD/MGH17.dat
@@ -1,93 +1,93 @@
-NIST/ITL StRD
-Dataset Name: MGH17 (MGH17.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 45)
- Certified Values (lines 41 to 50)
- Data (lines 61 to 93)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: This problem was found to be difficult for some very
- good algorithms.
-
- See More, J. J., Garbow, B. S., and Hillstrom, K. E.
- (1981). Testing unconstrained optimization software.
- ACM Transactions on Mathematical Software. 7(1):
- pp. 17-41.
-
-Reference: Osborne, M. R. (1972).
- Some aspects of nonlinear least squares
- calculations. In Numerical Methods for Nonlinear
- Optimization, Lootsma (Ed).
- New York, NY: Academic Press, pp. 171-189.
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 33 Observations
- Average Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 5 Parameters (b1 to b5)
-
- y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5] + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 50 0.5 3.7541005211E-01 2.0723153551E-03
- b2 = 150 1.5 1.9358469127E+00 2.2031669222E-01
- b3 = -100 -1 -1.4646871366E+00 2.2175707739E-01
- b4 = 1 0.01 1.2867534640E-02 4.4861358114E-04
- b5 = 2 0.02 2.2122699662E-02 8.9471996575E-04
-
-Residual Sum of Squares: 5.4648946975E-05
-Residual Standard Deviation: 1.3970497866E-03
-Degrees of Freedom: 28
-Number of Observations: 33
-
-
-
-
-
-
-
-
-
-Data: y x
- 8.440000E-01 0.000000E+00
- 9.080000E-01 1.000000E+01
- 9.320000E-01 2.000000E+01
- 9.360000E-01 3.000000E+01
- 9.250000E-01 4.000000E+01
- 9.080000E-01 5.000000E+01
- 8.810000E-01 6.000000E+01
- 8.500000E-01 7.000000E+01
- 8.180000E-01 8.000000E+01
- 7.840000E-01 9.000000E+01
- 7.510000E-01 1.000000E+02
- 7.180000E-01 1.100000E+02
- 6.850000E-01 1.200000E+02
- 6.580000E-01 1.300000E+02
- 6.280000E-01 1.400000E+02
- 6.030000E-01 1.500000E+02
- 5.800000E-01 1.600000E+02
- 5.580000E-01 1.700000E+02
- 5.380000E-01 1.800000E+02
- 5.220000E-01 1.900000E+02
- 5.060000E-01 2.000000E+02
- 4.900000E-01 2.100000E+02
- 4.780000E-01 2.200000E+02
- 4.670000E-01 2.300000E+02
- 4.570000E-01 2.400000E+02
- 4.480000E-01 2.500000E+02
- 4.380000E-01 2.600000E+02
- 4.310000E-01 2.700000E+02
- 4.240000E-01 2.800000E+02
- 4.200000E-01 2.900000E+02
- 4.140000E-01 3.000000E+02
- 4.110000E-01 3.100000E+02
- 4.060000E-01 3.200000E+02
+NIST/ITL StRD
+Dataset Name: MGH17 (MGH17.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 45)
+ Certified Values (lines 41 to 50)
+ Data (lines 61 to 93)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: This problem was found to be difficult for some very
+ good algorithms.
+
+ See More, J. J., Garbow, B. S., and Hillstrom, K. E.
+ (1981). Testing unconstrained optimization software.
+ ACM Transactions on Mathematical Software. 7(1):
+ pp. 17-41.
+
+Reference: Osborne, M. R. (1972).
+ Some aspects of nonlinear least squares
+ calculations. In Numerical Methods for Nonlinear
+ Optimization, Lootsma (Ed).
+ New York, NY: Academic Press, pp. 171-189.
+
+Data: 1 Response (y)
+ 1 Predictor (x)
+ 33 Observations
+ Average Level of Difficulty
+ Generated Data
+
+Model: Exponential Class
+ 5 Parameters (b1 to b5)
+
+ y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5] + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 50 0.5 3.7541005211E-01 2.0723153551E-03
+ b2 = 150 1.5 1.9358469127E+00 2.2031669222E-01
+ b3 = -100 -1 -1.4646871366E+00 2.2175707739E-01
+ b4 = 1 0.01 1.2867534640E-02 4.4861358114E-04
+ b5 = 2 0.02 2.2122699662E-02 8.9471996575E-04
+
+Residual Sum of Squares: 5.4648946975E-05
+Residual Standard Deviation: 1.3970497866E-03
+Degrees of Freedom: 28
+Number of Observations: 33
+
+
+
+
+
+
+
+
+
+Data: y x
+ 8.440000E-01 0.000000E+00
+ 9.080000E-01 1.000000E+01
+ 9.320000E-01 2.000000E+01
+ 9.360000E-01 3.000000E+01
+ 9.250000E-01 4.000000E+01
+ 9.080000E-01 5.000000E+01
+ 8.810000E-01 6.000000E+01
+ 8.500000E-01 7.000000E+01
+ 8.180000E-01 8.000000E+01
+ 7.840000E-01 9.000000E+01
+ 7.510000E-01 1.000000E+02
+ 7.180000E-01 1.100000E+02
+ 6.850000E-01 1.200000E+02
+ 6.580000E-01 1.300000E+02
+ 6.280000E-01 1.400000E+02
+ 6.030000E-01 1.500000E+02
+ 5.800000E-01 1.600000E+02
+ 5.580000E-01 1.700000E+02
+ 5.380000E-01 1.800000E+02
+ 5.220000E-01 1.900000E+02
+ 5.060000E-01 2.000000E+02
+ 4.900000E-01 2.100000E+02
+ 4.780000E-01 2.200000E+02
+ 4.670000E-01 2.300000E+02
+ 4.570000E-01 2.400000E+02
+ 4.480000E-01 2.500000E+02
+ 4.380000E-01 2.600000E+02
+ 4.310000E-01 2.700000E+02
+ 4.240000E-01 2.800000E+02
+ 4.200000E-01 2.900000E+02
+ 4.140000E-01 3.000000E+02
+ 4.110000E-01 3.100000E+02
+ 4.060000E-01 3.200000E+02
diff --git a/NIST_STRD/Misra1a.dat b/NIST_STRD/Misra1a.dat
index 332f37e..24f92a8 100644
--- a/NIST_STRD/Misra1a.dat
+++ b/NIST_STRD/Misra1a.dat
@@ -1,74 +1,74 @@
-NIST/ITL StRD
-Dataset Name: Misra1a (Misra1a.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 42)
- Certified Values (lines 41 to 47)
- Data (lines 61 to 74)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study regarding
- dental research in monomolecular adsorption. The
- response variable is volume, and the predictor
- variable is pressure.
-
-Reference: Misra, D., NIST (1978).
- Dental Research Monomolecular Adsorption Study.
-
-
-
-
-
-
-
-Data: 1 Response Variable (y = volume)
- 1 Predictor Variable (x = pressure)
- 14 Observations
- Lower Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 2 Parameters (b1 and b2)
-
- y = b1*(1-exp[-b2*x]) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 500 250 2.3894212918E+02 2.7070075241E+00
- b2 = 0.0001 0.0005 5.5015643181E-04 7.2668688436E-06
-
-Residual Sum of Squares: 1.2455138894E-01
-Residual Standard Deviation: 1.0187876330E-01
-Degrees of Freedom: 12
-Number of Observations: 14
-
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 10.07E0 77.6E0
- 14.73E0 114.9E0
- 17.94E0 141.1E0
- 23.93E0 190.8E0
- 29.61E0 239.9E0
- 35.18E0 289.0E0
- 40.02E0 332.8E0
- 44.82E0 378.4E0
- 50.76E0 434.8E0
- 55.05E0 477.3E0
- 61.01E0 536.8E0
- 66.40E0 593.1E0
- 75.47E0 689.1E0
- 81.78E0 760.0E0
+NIST/ITL StRD
+Dataset Name: Misra1a (Misra1a.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 42)
+ Certified Values (lines 41 to 47)
+ Data (lines 61 to 74)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are the result of a NIST study regarding
+ dental research in monomolecular adsorption. The
+ response variable is volume, and the predictor
+ variable is pressure.
+
+Reference: Misra, D., NIST (1978).
+ Dental Research Monomolecular Adsorption Study.
+
+
+
+
+
+
+
+Data: 1 Response Variable (y = volume)
+ 1 Predictor Variable (x = pressure)
+ 14 Observations
+ Lower Level of Difficulty
+ Observed Data
+
+Model: Exponential Class
+ 2 Parameters (b1 and b2)
+
+ y = b1*(1-exp[-b2*x]) + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 500 250 2.3894212918E+02 2.7070075241E+00
+ b2 = 0.0001 0.0005 5.5015643181E-04 7.2668688436E-06
+
+Residual Sum of Squares: 1.2455138894E-01
+Residual Standard Deviation: 1.0187876330E-01
+Degrees of Freedom: 12
+Number of Observations: 14
+
+
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 10.07E0 77.6E0
+ 14.73E0 114.9E0
+ 17.94E0 141.1E0
+ 23.93E0 190.8E0
+ 29.61E0 239.9E0
+ 35.18E0 289.0E0
+ 40.02E0 332.8E0
+ 44.82E0 378.4E0
+ 50.76E0 434.8E0
+ 55.05E0 477.3E0
+ 61.01E0 536.8E0
+ 66.40E0 593.1E0
+ 75.47E0 689.1E0
+ 81.78E0 760.0E0
diff --git a/NIST_STRD/Misra1b.dat b/NIST_STRD/Misra1b.dat
index 7923d40..a0da9d3 100644
--- a/NIST_STRD/Misra1b.dat
+++ b/NIST_STRD/Misra1b.dat
@@ -1,74 +1,74 @@
-NIST/ITL StRD
-Dataset Name: Misra1b (Misra1b.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 42)
- Certified Values (lines 41 to 47)
- Data (lines 61 to 74)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study regarding
- dental research in monomolecular adsorption. The
- response variable is volume, and the predictor
- variable is pressure.
-
-Reference: Misra, D., NIST (1978).
- Dental Research Monomolecular Adsorption Study.
-
-
-
-
-
-
-
-Data: 1 Response (y = volume)
- 1 Predictor (x = pressure)
- 14 Observations
- Lower Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 2 Parameters (b1 and b2)
-
- y = b1 * (1-(1+b2*x/2)**(-2)) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 500 300 3.3799746163E+02 3.1643950207E+00
- b2 = 0.0001 0.0002 3.9039091287E-04 4.2547321834E-06
-
-Residual Sum of Squares: 7.5464681533E-02
-Residual Standard Deviation: 7.9301471998E-02
-Degrees of Freedom: 12
-Number of Observations: 14
-
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 10.07E0 77.6E0
- 14.73E0 114.9E0
- 17.94E0 141.1E0
- 23.93E0 190.8E0
- 29.61E0 239.9E0
- 35.18E0 289.0E0
- 40.02E0 332.8E0
- 44.82E0 378.4E0
- 50.76E0 434.8E0
- 55.05E0 477.3E0
- 61.01E0 536.8E0
- 66.40E0 593.1E0
- 75.47E0 689.1E0
- 81.78E0 760.0E0
+NIST/ITL StRD
+Dataset Name: Misra1b (Misra1b.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 42)
+ Certified Values (lines 41 to 47)
+ Data (lines 61 to 74)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are the result of a NIST study regarding
+ dental research in monomolecular adsorption. The
+ response variable is volume, and the predictor
+ variable is pressure.
+
+Reference: Misra, D., NIST (1978).
+ Dental Research Monomolecular Adsorption Study.
+
+
+
+
+
+
+
+Data: 1 Response (y = volume)
+ 1 Predictor (x = pressure)
+ 14 Observations
+ Lower Level of Difficulty
+ Observed Data
+
+Model: Miscellaneous Class
+ 2 Parameters (b1 and b2)
+
+ y = b1 * (1-(1+b2*x/2)**(-2)) + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 500 300 3.3799746163E+02 3.1643950207E+00
+ b2 = 0.0001 0.0002 3.9039091287E-04 4.2547321834E-06
+
+Residual Sum of Squares: 7.5464681533E-02
+Residual Standard Deviation: 7.9301471998E-02
+Degrees of Freedom: 12
+Number of Observations: 14
+
+
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 10.07E0 77.6E0
+ 14.73E0 114.9E0
+ 17.94E0 141.1E0
+ 23.93E0 190.8E0
+ 29.61E0 239.9E0
+ 35.18E0 289.0E0
+ 40.02E0 332.8E0
+ 44.82E0 378.4E0
+ 50.76E0 434.8E0
+ 55.05E0 477.3E0
+ 61.01E0 536.8E0
+ 66.40E0 593.1E0
+ 75.47E0 689.1E0
+ 81.78E0 760.0E0
diff --git a/NIST_STRD/Misra1c.dat b/NIST_STRD/Misra1c.dat
index d86bc82..64681d3 100644
--- a/NIST_STRD/Misra1c.dat
+++ b/NIST_STRD/Misra1c.dat
@@ -1,74 +1,74 @@
-NIST/ITL StRD
-Dataset Name: Misra1c (Misra1c.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 42)
- Certified Values (lines 41 to 47)
- Data (lines 61 to 74)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study regarding
- dental research in monomolecular adsorption. The
- response variable is volume, and the predictor
- variable is pressure.
-
-Reference: Misra, D., NIST (1978).
- Dental Research Monomolecular Adsorption.
-
-
-
-
-
-
-
-Data: 1 Response (y = volume)
- 1 Predictor (x = pressure)
- 14 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 2 Parameters (b1 and b2)
-
- y = b1 * (1-(1+2*b2*x)**(-.5)) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 500 600 6.3642725809E+02 4.6638326572E+00
- b2 = 0.0001 0.0002 2.0813627256E-04 1.7728423155E-06
-
-Residual Sum of Squares: 4.0966836971E-02
-Residual Standard Deviation: 5.8428615257E-02
-Degrees of Freedom: 12
-Number of Observations: 14
-
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 10.07E0 77.6E0
- 14.73E0 114.9E0
- 17.94E0 141.1E0
- 23.93E0 190.8E0
- 29.61E0 239.9E0
- 35.18E0 289.0E0
- 40.02E0 332.8E0
- 44.82E0 378.4E0
- 50.76E0 434.8E0
- 55.05E0 477.3E0
- 61.01E0 536.8E0
- 66.40E0 593.1E0
- 75.47E0 689.1E0
- 81.78E0 760.0E0
+NIST/ITL StRD
+Dataset Name: Misra1c (Misra1c.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 42)
+ Certified Values (lines 41 to 47)
+ Data (lines 61 to 74)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are the result of a NIST study regarding
+ dental research in monomolecular adsorption. The
+ response variable is volume, and the predictor
+ variable is pressure.
+
+Reference: Misra, D., NIST (1978).
+ Dental Research Monomolecular Adsorption.
+
+
+
+
+
+
+
+Data: 1 Response (y = volume)
+ 1 Predictor (x = pressure)
+ 14 Observations
+ Average Level of Difficulty
+ Observed Data
+
+Model: Miscellaneous Class
+ 2 Parameters (b1 and b2)
+
+ y = b1 * (1-(1+2*b2*x)**(-.5)) + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 500 600 6.3642725809E+02 4.6638326572E+00
+ b2 = 0.0001 0.0002 2.0813627256E-04 1.7728423155E-06
+
+Residual Sum of Squares: 4.0966836971E-02
+Residual Standard Deviation: 5.8428615257E-02
+Degrees of Freedom: 12
+Number of Observations: 14
+
+
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 10.07E0 77.6E0
+ 14.73E0 114.9E0
+ 17.94E0 141.1E0
+ 23.93E0 190.8E0
+ 29.61E0 239.9E0
+ 35.18E0 289.0E0
+ 40.02E0 332.8E0
+ 44.82E0 378.4E0
+ 50.76E0 434.8E0
+ 55.05E0 477.3E0
+ 61.01E0 536.8E0
+ 66.40E0 593.1E0
+ 75.47E0 689.1E0
+ 81.78E0 760.0E0
diff --git a/NIST_STRD/Misra1d.dat b/NIST_STRD/Misra1d.dat
index 237de46..fcf12d3 100644
--- a/NIST_STRD/Misra1d.dat
+++ b/NIST_STRD/Misra1d.dat
@@ -1,74 +1,74 @@
-NIST/ITL StRD
-Dataset Name: Misra1d (Misra1d.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 42)
- Certified Values (lines 41 to 47)
- Data (lines 61 to 74)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study regarding
- dental research in monomolecular adsorption. The
- response variable is volume, and the predictor
- variable is pressure.
-
-Reference: Misra, D., NIST (1978).
- Dental Research Monomolecular Adsorption Study.
-
-
-
-
-
-
-
-Data: 1 Response (y = volume)
- 1 Predictor (x = pressure)
- 14 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 2 Parameters (b1 and b2)
-
- y = b1*b2*x*((1+b2*x)**(-1)) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 500 450 4.3736970754E+02 3.6489174345E+00
- b2 = 0.0001 0.0003 3.0227324449E-04 2.9334354479E-06
-
-Residual Sum of Squares: 5.6419295283E-02
-Residual Standard Deviation: 6.8568272111E-02
-Degrees of Freedom: 12
-Number of Observations: 14
-
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 10.07E0 77.6E0
- 14.73E0 114.9E0
- 17.94E0 141.1E0
- 23.93E0 190.8E0
- 29.61E0 239.9E0
- 35.18E0 289.0E0
- 40.02E0 332.8E0
- 44.82E0 378.4E0
- 50.76E0 434.8E0
- 55.05E0 477.3E0
- 61.01E0 536.8E0
- 66.40E0 593.1E0
- 75.47E0 689.1E0
- 81.78E0 760.0E0
+NIST/ITL StRD
+Dataset Name: Misra1d (Misra1d.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 42)
+ Certified Values (lines 41 to 47)
+ Data (lines 61 to 74)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are the result of a NIST study regarding
+ dental research in monomolecular adsorption. The
+ response variable is volume, and the predictor
+ variable is pressure.
+
+Reference: Misra, D., NIST (1978).
+ Dental Research Monomolecular Adsorption Study.
+
+
+
+
+
+
+
+Data: 1 Response (y = volume)
+ 1 Predictor (x = pressure)
+ 14 Observations
+ Average Level of Difficulty
+ Observed Data
+
+Model: Miscellaneous Class
+ 2 Parameters (b1 and b2)
+
+ y = b1*b2*x*((1+b2*x)**(-1)) + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 500 450 4.3736970754E+02 3.6489174345E+00
+ b2 = 0.0001 0.0003 3.0227324449E-04 2.9334354479E-06
+
+Residual Sum of Squares: 5.6419295283E-02
+Residual Standard Deviation: 6.8568272111E-02
+Degrees of Freedom: 12
+Number of Observations: 14
+
+
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 10.07E0 77.6E0
+ 14.73E0 114.9E0
+ 17.94E0 141.1E0
+ 23.93E0 190.8E0
+ 29.61E0 239.9E0
+ 35.18E0 289.0E0
+ 40.02E0 332.8E0
+ 44.82E0 378.4E0
+ 50.76E0 434.8E0
+ 55.05E0 477.3E0
+ 61.01E0 536.8E0
+ 66.40E0 593.1E0
+ 75.47E0 689.1E0
+ 81.78E0 760.0E0
diff --git a/NIST_STRD/Nelson.dat b/NIST_STRD/Nelson.dat
index 5ce1003..a6dc9e2 100644
--- a/NIST_STRD/Nelson.dat
+++ b/NIST_STRD/Nelson.dat
@@ -1,188 +1,188 @@
-NIST/ITL StRD
-Dataset Name: Nelson (Nelson.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 188)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a study involving
- the analysis of performance degradation data from
- accelerated tests, published in IEEE Transactions
- on Reliability. The response variable is dialectric
- breakdown strength in kilo-volts, and the predictor
- variables are time in weeks and temperature in degrees
- Celcius.
-
-
-Reference: Nelson, W. (1981).
- Analysis of Performance-Degradation Data.
- IEEE Transactions on Reliability.
- Vol. 2, R-30, No. 2, pp. 149-155.
-
-Data: 1 Response ( y = dialectric breakdown strength)
- 2 Predictors (x1 = time; x2 = temperature)
- 128 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 3 Parameters (b1 to b3)
-
- log[y] = b1 - b2*x1 * exp[-b3*x2] + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 2 2.5 2.5906836021E+00 1.9149996413E-02
- b2 = 0.0001 0.000000005 5.6177717026E-09 6.1124096540E-09
- b3 = -0.01 -0.05 -5.7701013174E-02 3.9572366543E-03
-
-Residual Sum of Squares: 3.7976833176E+00
-Residual Standard Deviation: 1.7430280130E-01
-Degrees of Freedom: 125
-Number of Observations: 128
-
-
-
-
-
-
-
-
-
-
-
-Data: y x1 x2
- 15.00E0 1E0 180E0
- 17.00E0 1E0 180E0
- 15.50E0 1E0 180E0
- 16.50E0 1E0 180E0
- 15.50E0 1E0 225E0
- 15.00E0 1E0 225E0
- 16.00E0 1E0 225E0
- 14.50E0 1E0 225E0
- 15.00E0 1E0 250E0
- 14.50E0 1E0 250E0
- 12.50E0 1E0 250E0
- 11.00E0 1E0 250E0
- 14.00E0 1E0 275E0
- 13.00E0 1E0 275E0
- 14.00E0 1E0 275E0
- 11.50E0 1E0 275E0
- 14.00E0 2E0 180E0
- 16.00E0 2E0 180E0
- 13.00E0 2E0 180E0
- 13.50E0 2E0 180E0
- 13.00E0 2E0 225E0
- 13.50E0 2E0 225E0
- 12.50E0 2E0 225E0
- 12.50E0 2E0 225E0
- 12.50E0 2E0 250E0
- 12.00E0 2E0 250E0
- 11.50E0 2E0 250E0
- 12.00E0 2E0 250E0
- 13.00E0 2E0 275E0
- 11.50E0 2E0 275E0
- 13.00E0 2E0 275E0
- 12.50E0 2E0 275E0
- 13.50E0 4E0 180E0
- 17.50E0 4E0 180E0
- 17.50E0 4E0 180E0
- 13.50E0 4E0 180E0
- 12.50E0 4E0 225E0
- 12.50E0 4E0 225E0
- 15.00E0 4E0 225E0
- 13.00E0 4E0 225E0
- 12.00E0 4E0 250E0
- 13.00E0 4E0 250E0
- 12.00E0 4E0 250E0
- 13.50E0 4E0 250E0
- 10.00E0 4E0 275E0
- 11.50E0 4E0 275E0
- 11.00E0 4E0 275E0
- 9.50E0 4E0 275E0
- 15.00E0 8E0 180E0
- 15.00E0 8E0 180E0
- 15.50E0 8E0 180E0
- 16.00E0 8E0 180E0
- 13.00E0 8E0 225E0
- 10.50E0 8E0 225E0
- 13.50E0 8E0 225E0
- 14.00E0 8E0 225E0
- 12.50E0 8E0 250E0
- 12.00E0 8E0 250E0
- 11.50E0 8E0 250E0
- 11.50E0 8E0 250E0
- 6.50E0 8E0 275E0
- 5.50E0 8E0 275E0
- 6.00E0 8E0 275E0
- 6.00E0 8E0 275E0
- 18.50E0 16E0 180E0
- 17.00E0 16E0 180E0
- 15.30E0 16E0 180E0
- 16.00E0 16E0 180E0
- 13.00E0 16E0 225E0
- 14.00E0 16E0 225E0
- 12.50E0 16E0 225E0
- 11.00E0 16E0 225E0
- 12.00E0 16E0 250E0
- 12.00E0 16E0 250E0
- 11.50E0 16E0 250E0
- 12.00E0 16E0 250E0
- 6.00E0 16E0 275E0
- 6.00E0 16E0 275E0
- 5.00E0 16E0 275E0
- 5.50E0 16E0 275E0
- 12.50E0 32E0 180E0
- 13.00E0 32E0 180E0
- 16.00E0 32E0 180E0
- 12.00E0 32E0 180E0
- 11.00E0 32E0 225E0
- 9.50E0 32E0 225E0
- 11.00E0 32E0 225E0
- 11.00E0 32E0 225E0
- 11.00E0 32E0 250E0
- 10.00E0 32E0 250E0
- 10.50E0 32E0 250E0
- 10.50E0 32E0 250E0
- 2.70E0 32E0 275E0
- 2.70E0 32E0 275E0
- 2.50E0 32E0 275E0
- 2.40E0 32E0 275E0
- 13.00E0 48E0 180E0
- 13.50E0 48E0 180E0
- 16.50E0 48E0 180E0
- 13.60E0 48E0 180E0
- 11.50E0 48E0 225E0
- 10.50E0 48E0 225E0
- 13.50E0 48E0 225E0
- 12.00E0 48E0 225E0
- 7.00E0 48E0 250E0
- 6.90E0 48E0 250E0
- 8.80E0 48E0 250E0
- 7.90E0 48E0 250E0
- 1.20E0 48E0 275E0
- 1.50E0 48E0 275E0
- 1.00E0 48E0 275E0
- 1.50E0 48E0 275E0
- 13.00E0 64E0 180E0
- 12.50E0 64E0 180E0
- 16.50E0 64E0 180E0
- 16.00E0 64E0 180E0
- 11.00E0 64E0 225E0
- 11.50E0 64E0 225E0
- 10.50E0 64E0 225E0
- 10.00E0 64E0 225E0
- 7.27E0 64E0 250E0
- 7.50E0 64E0 250E0
- 6.70E0 64E0 250E0
- 7.60E0 64E0 250E0
- 1.50E0 64E0 275E0
- 1.00E0 64E0 275E0
- 1.20E0 64E0 275E0
- 1.20E0 64E0 275E0
+NIST/ITL StRD
+Dataset Name: Nelson (Nelson.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 43)
+ Certified Values (lines 41 to 48)
+ Data (lines 61 to 188)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are the result of a study involving
+ the analysis of performance degradation data from
+ accelerated tests, published in IEEE Transactions
+ on Reliability. The response variable is dialectric
+ breakdown strength in kilo-volts, and the predictor
+ variables are time in weeks and temperature in degrees
+ Celcius.
+
+
+Reference: Nelson, W. (1981).
+ Analysis of Performance-Degradation Data.
+ IEEE Transactions on Reliability.
+ Vol. 2, R-30, No. 2, pp. 149-155.
+
+Data: 1 Response ( y = dialectric breakdown strength)
+ 2 Predictors (x1 = time; x2 = temperature)
+ 128 Observations
+ Average Level of Difficulty
+ Observed Data
+
+Model: Exponential Class
+ 3 Parameters (b1 to b3)
+
+ log[y] = b1 - b2*x1 * exp[-b3*x2] + e
+
+
+
+ Starting values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 2 2.5 2.5906836021E+00 1.9149996413E-02
+ b2 = 0.0001 0.000000005 5.6177717026E-09 6.1124096540E-09
+ b3 = -0.01 -0.05 -5.7701013174E-02 3.9572366543E-03
+
+Residual Sum of Squares: 3.7976833176E+00
+Residual Standard Deviation: 1.7430280130E-01
+Degrees of Freedom: 125
+Number of Observations: 128
+
+
+
+
+
+
+
+
+
+
+
+Data: y x1 x2
+ 15.00E0 1E0 180E0
+ 17.00E0 1E0 180E0
+ 15.50E0 1E0 180E0
+ 16.50E0 1E0 180E0
+ 15.50E0 1E0 225E0
+ 15.00E0 1E0 225E0
+ 16.00E0 1E0 225E0
+ 14.50E0 1E0 225E0
+ 15.00E0 1E0 250E0
+ 14.50E0 1E0 250E0
+ 12.50E0 1E0 250E0
+ 11.00E0 1E0 250E0
+ 14.00E0 1E0 275E0
+ 13.00E0 1E0 275E0
+ 14.00E0 1E0 275E0
+ 11.50E0 1E0 275E0
+ 14.00E0 2E0 180E0
+ 16.00E0 2E0 180E0
+ 13.00E0 2E0 180E0
+ 13.50E0 2E0 180E0
+ 13.00E0 2E0 225E0
+ 13.50E0 2E0 225E0
+ 12.50E0 2E0 225E0
+ 12.50E0 2E0 225E0
+ 12.50E0 2E0 250E0
+ 12.00E0 2E0 250E0
+ 11.50E0 2E0 250E0
+ 12.00E0 2E0 250E0
+ 13.00E0 2E0 275E0
+ 11.50E0 2E0 275E0
+ 13.00E0 2E0 275E0
+ 12.50E0 2E0 275E0
+ 13.50E0 4E0 180E0
+ 17.50E0 4E0 180E0
+ 17.50E0 4E0 180E0
+ 13.50E0 4E0 180E0
+ 12.50E0 4E0 225E0
+ 12.50E0 4E0 225E0
+ 15.00E0 4E0 225E0
+ 13.00E0 4E0 225E0
+ 12.00E0 4E0 250E0
+ 13.00E0 4E0 250E0
+ 12.00E0 4E0 250E0
+ 13.50E0 4E0 250E0
+ 10.00E0 4E0 275E0
+ 11.50E0 4E0 275E0
+ 11.00E0 4E0 275E0
+ 9.50E0 4E0 275E0
+ 15.00E0 8E0 180E0
+ 15.00E0 8E0 180E0
+ 15.50E0 8E0 180E0
+ 16.00E0 8E0 180E0
+ 13.00E0 8E0 225E0
+ 10.50E0 8E0 225E0
+ 13.50E0 8E0 225E0
+ 14.00E0 8E0 225E0
+ 12.50E0 8E0 250E0
+ 12.00E0 8E0 250E0
+ 11.50E0 8E0 250E0
+ 11.50E0 8E0 250E0
+ 6.50E0 8E0 275E0
+ 5.50E0 8E0 275E0
+ 6.00E0 8E0 275E0
+ 6.00E0 8E0 275E0
+ 18.50E0 16E0 180E0
+ 17.00E0 16E0 180E0
+ 15.30E0 16E0 180E0
+ 16.00E0 16E0 180E0
+ 13.00E0 16E0 225E0
+ 14.00E0 16E0 225E0
+ 12.50E0 16E0 225E0
+ 11.00E0 16E0 225E0
+ 12.00E0 16E0 250E0
+ 12.00E0 16E0 250E0
+ 11.50E0 16E0 250E0
+ 12.00E0 16E0 250E0
+ 6.00E0 16E0 275E0
+ 6.00E0 16E0 275E0
+ 5.00E0 16E0 275E0
+ 5.50E0 16E0 275E0
+ 12.50E0 32E0 180E0
+ 13.00E0 32E0 180E0
+ 16.00E0 32E0 180E0
+ 12.00E0 32E0 180E0
+ 11.00E0 32E0 225E0
+ 9.50E0 32E0 225E0
+ 11.00E0 32E0 225E0
+ 11.00E0 32E0 225E0
+ 11.00E0 32E0 250E0
+ 10.00E0 32E0 250E0
+ 10.50E0 32E0 250E0
+ 10.50E0 32E0 250E0
+ 2.70E0 32E0 275E0
+ 2.70E0 32E0 275E0
+ 2.50E0 32E0 275E0
+ 2.40E0 32E0 275E0
+ 13.00E0 48E0 180E0
+ 13.50E0 48E0 180E0
+ 16.50E0 48E0 180E0
+ 13.60E0 48E0 180E0
+ 11.50E0 48E0 225E0
+ 10.50E0 48E0 225E0
+ 13.50E0 48E0 225E0
+ 12.00E0 48E0 225E0
+ 7.00E0 48E0 250E0
+ 6.90E0 48E0 250E0
+ 8.80E0 48E0 250E0
+ 7.90E0 48E0 250E0
+ 1.20E0 48E0 275E0
+ 1.50E0 48E0 275E0
+ 1.00E0 48E0 275E0
+ 1.50E0 48E0 275E0
+ 13.00E0 64E0 180E0
+ 12.50E0 64E0 180E0
+ 16.50E0 64E0 180E0
+ 16.00E0 64E0 180E0
+ 11.00E0 64E0 225E0
+ 11.50E0 64E0 225E0
+ 10.50E0 64E0 225E0
+ 10.00E0 64E0 225E0
+ 7.27E0 64E0 250E0
+ 7.50E0 64E0 250E0
+ 6.70E0 64E0 250E0
+ 7.60E0 64E0 250E0
+ 1.50E0 64E0 275E0
+ 1.00E0 64E0 275E0
+ 1.20E0 64E0 275E0
+ 1.20E0 64E0 275E0
diff --git a/NIST_STRD/Rat42.dat b/NIST_STRD/Rat42.dat
index e112fbb..5468df8 100644
--- a/NIST_STRD/Rat42.dat
+++ b/NIST_STRD/Rat42.dat
@@ -1,69 +1,69 @@
-NIST/ITL StRD
-Dataset Name: Rat42 (Rat42.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 69)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: This model and data are an example of fitting
- sigmoidal growth curves taken from Ratkowsky (1983).
- The response variable is pasture yield, and the
- predictor variable is growing time.
-
-
-Reference: Ratkowsky, D.A. (1983).
- Nonlinear Regression Modeling.
- New York, NY: Marcel Dekker, pp. 61 and 88.
-
-
-
-
-
-Data: 1 Response (y = pasture yield)
- 1 Predictor (x = growing time)
- 9 Observations
- Higher Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 3 Parameters (b1 to b3)
-
- y = b1 / (1+exp[b2-b3*x]) + e
-
-
-
- Starting Values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 100 75 7.2462237576E+01 1.7340283401E+00
- b2 = 1 2.5 2.6180768402E+00 8.8295217536E-02
- b3 = 0.1 0.07 6.7359200066E-02 3.4465663377E-03
-
-Residual Sum of Squares: 8.0565229338E+00
-Residual Standard Deviation: 1.1587725499E+00
-Degrees of Freedom: 6
-Number of Observations: 9
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 8.930E0 9.000E0
- 10.800E0 14.000E0
- 18.590E0 21.000E0
- 22.330E0 28.000E0
- 39.350E0 42.000E0
- 56.110E0 57.000E0
- 61.730E0 63.000E0
- 64.620E0 70.000E0
- 67.080E0 79.000E0
+NIST/ITL StRD
+Dataset Name: Rat42 (Rat42.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 43)
+ Certified Values (lines 41 to 48)
+ Data (lines 61 to 69)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: This model and data are an example of fitting
+ sigmoidal growth curves taken from Ratkowsky (1983).
+ The response variable is pasture yield, and the
+ predictor variable is growing time.
+
+
+Reference: Ratkowsky, D.A. (1983).
+ Nonlinear Regression Modeling.
+ New York, NY: Marcel Dekker, pp. 61 and 88.
+
+
+
+
+
+Data: 1 Response (y = pasture yield)
+ 1 Predictor (x = growing time)
+ 9 Observations
+ Higher Level of Difficulty
+ Observed Data
+
+Model: Exponential Class
+ 3 Parameters (b1 to b3)
+
+ y = b1 / (1+exp[b2-b3*x]) + e
+
+
+
+ Starting Values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 100 75 7.2462237576E+01 1.7340283401E+00
+ b2 = 1 2.5 2.6180768402E+00 8.8295217536E-02
+ b3 = 0.1 0.07 6.7359200066E-02 3.4465663377E-03
+
+Residual Sum of Squares: 8.0565229338E+00
+Residual Standard Deviation: 1.1587725499E+00
+Degrees of Freedom: 6
+Number of Observations: 9
+
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 8.930E0 9.000E0
+ 10.800E0 14.000E0
+ 18.590E0 21.000E0
+ 22.330E0 28.000E0
+ 39.350E0 42.000E0
+ 56.110E0 57.000E0
+ 61.730E0 63.000E0
+ 64.620E0 70.000E0
+ 67.080E0 79.000E0
diff --git a/NIST_STRD/Rat43.dat b/NIST_STRD/Rat43.dat
index 347d846..ca6d1dc 100644
--- a/NIST_STRD/Rat43.dat
+++ b/NIST_STRD/Rat43.dat
@@ -1,75 +1,75 @@
-NIST/ITL StRD
-Dataset Name: Rat43 (Rat43.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 44)
- Certified Values (lines 41 to 49)
- Data (lines 61 to 75)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: This model and data are an example of fitting
- sigmoidal growth curves taken from Ratkowsky (1983).
- The response variable is the dry weight of onion bulbs
- and tops, and the predictor variable is growing time.
-
-
-Reference: Ratkowsky, D.A. (1983).
- Nonlinear Regression Modeling.
- New York, NY: Marcel Dekker, pp. 62 and 88.
-
-
-
-
-
-Data: 1 Response (y = onion bulb dry weight)
- 1 Predictor (x = growing time)
- 15 Observations
- Higher Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 4 Parameters (b1 to b4)
-
- y = b1 / ((1+exp[b2-b3*x])**(1/b4)) + e
-
-
-
- Starting Values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 100 700 6.9964151270E+02 1.6302297817E+01
- b2 = 10 5 5.2771253025E+00 2.0828735829E+00
- b3 = 1 0.75 7.5962938329E-01 1.9566123451E-01
- b4 = 1 1.3 1.2792483859E+00 6.8761936385E-01
-
-Residual Sum of Squares: 8.7864049080E+03
-Residual Standard Deviation: 2.8262414662E+01
-Degrees of Freedom: 9
-Number of Observations: 15
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 16.08E0 1.0E0
- 33.83E0 2.0E0
- 65.80E0 3.0E0
- 97.20E0 4.0E0
- 191.55E0 5.0E0
- 326.20E0 6.0E0
- 386.87E0 7.0E0
- 520.53E0 8.0E0
- 590.03E0 9.0E0
- 651.92E0 10.0E0
- 724.93E0 11.0E0
- 699.56E0 12.0E0
- 689.96E0 13.0E0
- 637.56E0 14.0E0
- 717.41E0 15.0E0
+NIST/ITL StRD
+Dataset Name: Rat43 (Rat43.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 44)
+ Certified Values (lines 41 to 49)
+ Data (lines 61 to 75)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: This model and data are an example of fitting
+ sigmoidal growth curves taken from Ratkowsky (1983).
+ The response variable is the dry weight of onion bulbs
+ and tops, and the predictor variable is growing time.
+
+
+Reference: Ratkowsky, D.A. (1983).
+ Nonlinear Regression Modeling.
+ New York, NY: Marcel Dekker, pp. 62 and 88.
+
+
+
+
+
+Data: 1 Response (y = onion bulb dry weight)
+ 1 Predictor (x = growing time)
+ 15 Observations
+ Higher Level of Difficulty
+ Observed Data
+
+Model: Exponential Class
+ 4 Parameters (b1 to b4)
+
+ y = b1 / ((1+exp[b2-b3*x])**(1/b4)) + e
+
+
+
+ Starting Values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 100 700 6.9964151270E+02 1.6302297817E+01
+ b2 = 10 5 5.2771253025E+00 2.0828735829E+00
+ b3 = 1 0.75 7.5962938329E-01 1.9566123451E-01
+ b4 = 1 1.3 1.2792483859E+00 6.8761936385E-01
+
+Residual Sum of Squares: 8.7864049080E+03
+Residual Standard Deviation: 2.8262414662E+01
+Degrees of Freedom: 9
+Number of Observations: 15
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 16.08E0 1.0E0
+ 33.83E0 2.0E0
+ 65.80E0 3.0E0
+ 97.20E0 4.0E0
+ 191.55E0 5.0E0
+ 326.20E0 6.0E0
+ 386.87E0 7.0E0
+ 520.53E0 8.0E0
+ 590.03E0 9.0E0
+ 651.92E0 10.0E0
+ 724.93E0 11.0E0
+ 699.56E0 12.0E0
+ 689.96E0 13.0E0
+ 637.56E0 14.0E0
+ 717.41E0 15.0E0
diff --git a/NIST_STRD/Roszman1.dat b/NIST_STRD/Roszman1.dat
index 0296837..ddab210 100644
--- a/NIST_STRD/Roszman1.dat
+++ b/NIST_STRD/Roszman1.dat
@@ -1,85 +1,85 @@
-NIST/ITL StRD
-Dataset Name: Roszman1 (Roszman1.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 44)
- Certified Values (lines 41 to 49)
- Data (lines 61 to 85)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- quantum defects in iodine atoms. The response
- variable is the number of quantum defects, and the
- predictor variable is the excited energy state.
- The argument to the ARCTAN function is in radians.
-
-Reference: Roszman, L., NIST (19??).
- Quantum Defects for Sulfur I Atom.
-
-
-
-
-
-
-Data: 1 Response (y = quantum defect)
- 1 Predictor (x = excited state energy)
- 25 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 4 Parameters (b1 to b4)
-
- pi = 3.141592653589793238462643383279E0
- y = b1 - b2*x - arctan[b3/(x-b4)]/pi + e
-
-
- Starting Values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 0.1 0.2 2.0196866396E-01 1.9172666023E-02
- b2 = -0.00001 -0.000005 -6.1953516256E-06 3.2058931691E-06
- b3 = 1000 1200 1.2044556708E+03 7.4050983057E+01
- b4 = -100 -150 -1.8134269537E+02 4.9573513849E+01
-
-Residual Sum of Squares: 4.9484847331E-04
-Residual Standard Deviation: 4.8542984060E-03
-Degrees of Freedom: 21
-Number of Observations: 25
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 0.252429 -4868.68
- 0.252141 -4868.09
- 0.251809 -4867.41
- 0.297989 -3375.19
- 0.296257 -3373.14
- 0.295319 -3372.03
- 0.339603 -2473.74
- 0.337731 -2472.35
- 0.333820 -2469.45
- 0.389510 -1894.65
- 0.386998 -1893.40
- 0.438864 -1497.24
- 0.434887 -1495.85
- 0.427893 -1493.41
- 0.471568 -1208.68
- 0.461699 -1206.18
- 0.461144 -1206.04
- 0.513532 -997.92
- 0.506641 -996.61
- 0.505062 -996.31
- 0.535648 -834.94
- 0.533726 -834.66
- 0.568064 -710.03
- 0.612886 -530.16
- 0.624169 -464.17
+NIST/ITL StRD
+Dataset Name: Roszman1 (Roszman1.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 44)
+ Certified Values (lines 41 to 49)
+ Data (lines 61 to 85)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are the result of a NIST study involving
+ quantum defects in iodine atoms. The response
+ variable is the number of quantum defects, and the
+ predictor variable is the excited energy state.
+ The argument to the ARCTAN function is in radians.
+
+Reference: Roszman, L., NIST (19??).
+ Quantum Defects for Sulfur I Atom.
+
+
+
+
+
+
+Data: 1 Response (y = quantum defect)
+ 1 Predictor (x = excited state energy)
+ 25 Observations
+ Average Level of Difficulty
+ Observed Data
+
+Model: Miscellaneous Class
+ 4 Parameters (b1 to b4)
+
+ pi = 3.141592653589793238462643383279E0
+ y = b1 - b2*x - arctan[b3/(x-b4)]/pi + e
+
+
+ Starting Values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 0.1 0.2 2.0196866396E-01 1.9172666023E-02
+ b2 = -0.00001 -0.000005 -6.1953516256E-06 3.2058931691E-06
+ b3 = 1000 1200 1.2044556708E+03 7.4050983057E+01
+ b4 = -100 -150 -1.8134269537E+02 4.9573513849E+01
+
+Residual Sum of Squares: 4.9484847331E-04
+Residual Standard Deviation: 4.8542984060E-03
+Degrees of Freedom: 21
+Number of Observations: 25
+
+
+
+
+
+
+
+
+
+
+Data: y x
+ 0.252429 -4868.68
+ 0.252141 -4868.09
+ 0.251809 -4867.41
+ 0.297989 -3375.19
+ 0.296257 -3373.14
+ 0.295319 -3372.03
+ 0.339603 -2473.74
+ 0.337731 -2472.35
+ 0.333820 -2469.45
+ 0.389510 -1894.65
+ 0.386998 -1893.40
+ 0.438864 -1497.24
+ 0.434887 -1495.85
+ 0.427893 -1493.41
+ 0.471568 -1208.68
+ 0.461699 -1206.18
+ 0.461144 -1206.04
+ 0.513532 -997.92
+ 0.506641 -996.61
+ 0.505062 -996.31
+ 0.535648 -834.94
+ 0.533726 -834.66
+ 0.568064 -710.03
+ 0.612886 -530.16
+ 0.624169 -464.17
diff --git a/NIST_STRD/Thurber.dat b/NIST_STRD/Thurber.dat
index 6d72fd9..6ecdc77 100644
--- a/NIST_STRD/Thurber.dat
+++ b/NIST_STRD/Thurber.dat
@@ -1,97 +1,97 @@
-NIST/ITL StRD
-Dataset Name: Thurber (Thurber.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 47)
- Certified Values (lines 41 to 52)
- Data (lines 61 to 97)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- semiconductor electron mobility. The response
- variable is a measure of electron mobility, and the
- predictor variable is the natural log of the density.
-
-
-Reference: Thurber, R., NIST (197?).
- Semiconductor electron mobility modeling.
-
-
-
-
-
-
-Data: 1 Response Variable (y = electron mobility)
- 1 Predictor Variable (x = log[density])
- 37 Observations
- Higher Level of Difficulty
- Observed Data
-
-Model: Rational Class (cubic/cubic)
- 7 Parameters (b1 to b7)
-
- y = (b1 + b2*x + b3*x**2 + b4*x**3) /
- (1 + b5*x + b6*x**2 + b7*x**3) + e
-
-
- Starting Values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1000 1300 1.2881396800E+03 4.6647963344E+00
- b2 = 1000 1500 1.4910792535E+03 3.9571156086E+01
- b3 = 400 500 5.8323836877E+02 2.8698696102E+01
- b4 = 40 75 7.5416644291E+01 5.5675370270E+00
- b5 = 0.7 1 9.6629502864E-01 3.1333340687E-02
- b6 = 0.3 0.4 3.9797285797E-01 1.4984928198E-02
- b7 = 0.03 0.05 4.9727297349E-02 6.5842344623E-03
-
-Residual Sum of Squares: 5.6427082397E+03
-Residual Standard Deviation: 1.3714600784E+01
-Degrees of Freedom: 30
-Number of Observations: 37
-
-
-
-
-
-
-
-Data: y x
- 80.574E0 -3.067E0
- 84.248E0 -2.981E0
- 87.264E0 -2.921E0
- 87.195E0 -2.912E0
- 89.076E0 -2.840E0
- 89.608E0 -2.797E0
- 89.868E0 -2.702E0
- 90.101E0 -2.699E0
- 92.405E0 -2.633E0
- 95.854E0 -2.481E0
- 100.696E0 -2.363E0
- 101.060E0 -2.322E0
- 401.672E0 -1.501E0
- 390.724E0 -1.460E0
- 567.534E0 -1.274E0
- 635.316E0 -1.212E0
- 733.054E0 -1.100E0
- 759.087E0 -1.046E0
- 894.206E0 -0.915E0
- 990.785E0 -0.714E0
- 1090.109E0 -0.566E0
- 1080.914E0 -0.545E0
- 1122.643E0 -0.400E0
- 1178.351E0 -0.309E0
- 1260.531E0 -0.109E0
- 1273.514E0 -0.103E0
- 1288.339E0 0.010E0
- 1327.543E0 0.119E0
- 1353.863E0 0.377E0
- 1414.509E0 0.790E0
- 1425.208E0 0.963E0
- 1421.384E0 1.006E0
- 1442.962E0 1.115E0
- 1464.350E0 1.572E0
- 1468.705E0 1.841E0
- 1447.894E0 2.047E0
- 1457.628E0 2.200E0
+NIST/ITL StRD
+Dataset Name: Thurber (Thurber.dat)
+
+File Format: ASCII
+ Starting Values (lines 41 to 47)
+ Certified Values (lines 41 to 52)
+ Data (lines 61 to 97)
+
+Procedure: Nonlinear Least Squares Regression
+
+Description: These data are the result of a NIST study involving
+ semiconductor electron mobility. The response
+ variable is a measure of electron mobility, and the
+ predictor variable is the natural log of the density.
+
+
+Reference: Thurber, R., NIST (197?).
+ Semiconductor electron mobility modeling.
+
+
+
+
+
+
+Data: 1 Response Variable (y = electron mobility)
+ 1 Predictor Variable (x = log[density])
+ 37 Observations
+ Higher Level of Difficulty
+ Observed Data
+
+Model: Rational Class (cubic/cubic)
+ 7 Parameters (b1 to b7)
+
+ y = (b1 + b2*x + b3*x**2 + b4*x**3) /
+ (1 + b5*x + b6*x**2 + b7*x**3) + e
+
+
+ Starting Values Certified Values
+
+ Start 1 Start 2 Parameter Standard Deviation
+ b1 = 1000 1300 1.2881396800E+03 4.6647963344E+00
+ b2 = 1000 1500 1.4910792535E+03 3.9571156086E+01
+ b3 = 400 500 5.8323836877E+02 2.8698696102E+01
+ b4 = 40 75 7.5416644291E+01 5.5675370270E+00
+ b5 = 0.7 1 9.6629502864E-01 3.1333340687E-02
+ b6 = 0.3 0.4 3.9797285797E-01 1.4984928198E-02
+ b7 = 0.03 0.05 4.9727297349E-02 6.5842344623E-03
+
+Residual Sum of Squares: 5.6427082397E+03
+Residual Standard Deviation: 1.3714600784E+01
+Degrees of Freedom: 30
+Number of Observations: 37
+
+
+
+
+
+
+
+Data: y x
+ 80.574E0 -3.067E0
+ 84.248E0 -2.981E0
+ 87.264E0 -2.921E0
+ 87.195E0 -2.912E0
+ 89.076E0 -2.840E0
+ 89.608E0 -2.797E0
+ 89.868E0 -2.702E0
+ 90.101E0 -2.699E0
+ 92.405E0 -2.633E0
+ 95.854E0 -2.481E0
+ 100.696E0 -2.363E0
+ 101.060E0 -2.322E0
+ 401.672E0 -1.501E0
+ 390.724E0 -1.460E0
+ 567.534E0 -1.274E0
+ 635.316E0 -1.212E0
+ 733.054E0 -1.100E0
+ 759.087E0 -1.046E0
+ 894.206E0 -0.915E0
+ 990.785E0 -0.714E0
+ 1090.109E0 -0.566E0
+ 1080.914E0 -0.545E0
+ 1122.643E0 -0.400E0
+ 1178.351E0 -0.309E0
+ 1260.531E0 -0.109E0
+ 1273.514E0 -0.103E0
+ 1288.339E0 0.010E0
+ 1327.543E0 0.119E0
+ 1353.863E0 0.377E0
+ 1414.509E0 0.790E0
+ 1425.208E0 0.963E0
+ 1421.384E0 1.006E0
+ 1442.962E0 1.115E0
+ 1464.350E0 1.572E0
+ 1468.705E0 1.841E0
+ 1447.894E0 2.047E0
+ 1457.628E0 2.200E0
diff --git a/PKG-INFO b/PKG-INFO
index 7c27e7d..3842e9b 100644
--- a/PKG-INFO
+++ b/PKG-INFO
@@ -1,6 +1,6 @@
Metadata-Version: 1.1
Name: lmfit
-Version: 0.9.2
+Version: 0.9.3
Summary: Least-Squares Minimization with Bounds and Constraints
Home-page: http://lmfit.github.io/lmfit-py/
Author: LMFit Development Team
diff --git a/README b/README
deleted file mode 100644
index eacaee5..0000000
--- a/README
+++ /dev/null
@@ -1,65 +0,0 @@
-LMfit-py
-========
-
-[](https://travis-ci.org/lmfit/lmfit-py)
-
-LMfit-py provides a Least-Squares Minimization routine and class
-with a simple, flexible approach to parameterizing a model for
-fitting to data. Named Parameters can be held fixed or freely
-adjusted in the fit, or held between lower and upper bounds. In
-addition, parameters can be constrained as a simple mathematical
-expression of other Parameters.
-
-To do this, the programmer defines a Parameters object, an enhanced
-dictionary, containing named parameters:
-
- fit_params = Parameters()
- fit_params['amp'] = Parameter(value=1.2, min=0.1, max=1000)
- fit_params['cen'] = Parameter(value=40.0, vary=False),
- fit_params['wid'] = Parameter(value=4, min=0)}
-
-or using the equivalent
-
- fit_params = Parameters()
- fit_params.add('amp', value=1.2, min=0.1, max=1000)
- fit_params.add('cen', value=40.0, vary=False),
- fit_params.add('wid', value=4, min=0)
-
-The programmer will also write a function to be minimized (in the
-least-squares sense) with its first argument being this Parameters object,
-and additional positional and keyword arguments as desired:
-
- def myfunc(params, x, data, someflag=True):
- amp = params['amp'].value
- cen = params['cen'].value
- wid = params['wid'].value
- ...
- return residual_array
-
-For each call of this function, the values for the params may have changed,
-subject to the bounds and constraint settings for each Parameter. The function
-should return the residual (ie, data-model) array to be minimized.
-
-The advantage here is that the function to be minimized does not have to be
-changed if different bounds or constraints are placed on the fitting
-Parameters. The fitting model (as described in myfunc) is instead written
-in terms of physical parameters of the system, and remains remains
-independent of what is actually varied in the fit. In addition, which
-parameters are adjuested and which are fixed happens at run-time, so that
-changing what is varied and what constraints are placed on the parameters
-can easily be modified by the consumer in real-time data analysis.
-
-To perform the fit, the user calls
-
- result = minimize(myfunc, fit_params, args=(x, data), kws={'someflag':True}, ....)
-
-After the fit, each real variable in the ``fit_params`` dictionary is updated
-to have best-fit values, estimated standard deviations, and correlations
-with other variables in the fit, while the results dictionary holds fit
-statistics and information.
-
-By default, the underlying fit algorithm is the Levenberg-Marquart
-algorithm with numerically-calculated derivatives from MINPACK's lmdif
-function, as used by scipy.optimize.leastsq. Other solvers (currently
-Simulated Annealing and L-BFGS-B) are also available, though slightly less
-well-tested and supported.
diff --git a/THANKS.txt b/THANKS.txt
index 4436a80..b208054 100644
--- a/THANKS.txt
+++ b/THANKS.txt
@@ -1,24 +1,24 @@
-Many people have contributed to lmfit.
-
-Matthew Newville wrote the original version and maintains the project.
-Till Stensitzki wrote the improved estimates of confidence intervals, and
- contributed many tests, bug fixes, and documentation.
-Daniel B. Allan wrote much of the high level Model code, and many
- improvements to the testing and documentation.
-Antonino Ingargiola wrote much of the high level Model code and provided
- many bug fixes.
-J. J. Helmus wrote the MINUT bounds for leastsq, originally in
- leastsqbounds.py, and ported to lmfit.
-E. O. Le Bigot wrote the uncertainties package, a version of which is used
- by lmfit.
-Michal Rawlik added plotting capabilities for Models.
-A. R. J. Nelson added differential_evolution, and greatly improved the code
- in the docstrings.
-
-Additional patches, bug fixes, and suggestions have come from Christoph
- Deil, Francois Boulogne, Thomas Caswell, Colin Brosseau, nmearl,
- Gustavo Pasquevich, Clemens Prescher, LiCode, and Ben Gamari.
-
-The lmfit code obviously depends on, and owes a very large debt to the code
-in scipy.optimize. Several discussions on the scipy-user and lmfit mailing
-lists have also led to improvements in this code.
+Many people have contributed to lmfit.
+
+Matthew Newville wrote the original version and maintains the project.
+Till Stensitzki wrote the improved estimates of confidence intervals, and
+ contributed many tests, bug fixes, and documentation.
+Daniel B. Allan wrote much of the high level Model code, and many
+ improvements to the testing and documentation.
+Antonino Ingargiola wrote much of the high level Model code and provided
+ many bug fixes.
+J. J. Helmus wrote the MINUT bounds for leastsq, originally in
+ leastsqbounds.py, and ported to lmfit.
+E. O. Le Bigot wrote the uncertainties package, a version of which is used
+ by lmfit.
+Michal Rawlik added plotting capabilities for Models.
+A. R. J. Nelson added differential_evolution, emcee, and greatly improved the
+ code in the docstrings.
+
+Additional patches, bug fixes, and suggestions have come from Christoph
+ Deil, Francois Boulogne, Thomas Caswell, Colin Brosseau, nmearl,
+ Gustavo Pasquevich, Clemens Prescher, LiCode, and Ben Gamari.
+
+The lmfit code obviously depends on, and owes a very large debt to the code
+in scipy.optimize. Several discussions on the scipy-user and lmfit mailing
+lists have also led to improvements in this code.
diff --git a/doc/Makefile b/doc/Makefile
index 5add84d..1c72ec9 100644
--- a/doc/Makefile
+++ b/doc/Makefile
@@ -1,112 +1,112 @@
-# Makefile for Sphinx documentation
-#
-
-# You can set these variables from the command line.
-SPHINXOPTS =
-SPHINXBUILD = sphinx-build
-PAPER =
-BUILDDIR = _build
-INSTALLDIR = /home/newville/public_html/lmfit/
-
-
-# Internal variables.
-PAPEROPT_a4 = -D latex_paper_size=a4
-PAPEROPT_letter = -D latex_paper_size=letter
-ALLSPHINXOPTS = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) .
-
-.PHONY: help clean html dirhtml pickle json htmlhelp qthelp latex changes linkcheck doctest latexpdf htmlzip
-.PHONY: all install pdf
-
-html:
- cp sphinx/ext_mathjax.py extensions.py
- $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html
- @echo
- @echo "html build finished: $(BUILDDIR)/html."
-
-htmlzip: html
- cp sphinx/ext_pngmath.py extensions.py
- $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/lmfit_doc
- cd $(BUILDDIR) && zip -pur html/lmfit_doc.zip lmfit_doc
-
-epub:
- cp sphinx/ext_pngmath.py extensions.py
- $(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) $(BUILDDIR)/epub
- cp -pr $(BUILDDIR)/epub/*.epub $(BUILDDIR)/html/.
-
-pdf: latex
- cd $(BUILDDIR)/latex && make all-pdf
- cp -pr $(BUILDDIR)/latex/lmfit.pdf $(BUILDDIR)/html/.
-
-all: html htmlzip epub pdf
-
-install: all
- cd $(BUILDDIR)/latex && pdflatex lmfit.tex
- cd $(BUILDDIR)/latex && makeindex -s python.ist lmfit.idx
- cd $(BUILDDIR)/latex && pdflatex lmfit.tex
- cp -pr $(BUILDDIR)/html/* $(INSTALLDIR)/.
-
-help:
- @echo "Please use \`make <target>' where <target> is one of"
- @echo " html to make standalone HTML files"
- @echo " dirhtml to make HTML files named index.html in directories"
- @echo " pickle to make pickle files"
- @echo " json to make JSON files"
- @echo " htmlhelp to make HTML files and a HTML help project"
- @echo " qthelp to make HTML files and a qthelp project"
- @echo " latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter"
- @echo " changes to make an overview of all changed/added/deprecated items"
- @echo " linkcheck to check all external links for integrity"
- @echo " doctest to run all doctests embedded in the documentation (if enabled)"
-
-clean:
- -rm -rf $(BUILDDIR)/*
-
-dirhtml:
- $(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml
- @echo
- @echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml."
-
-pickle:
- $(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle
- @echo
- @echo "Build finished; now you can process the pickle files."
-
-json:
- $(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json
- @echo
- @echo "Build finished; now you can process the JSON files."
-
-htmlhelp:
- $(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp
- @echo
- @echo "Build finished; now you can run HTML Help Workshop with the" \
- ".hhp project file in $(BUILDDIR)/htmlhelp."
-
-latex:
- $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) _build/latex
- @echo
- @echo "Build finished; the LaTeX files are in _build/latex."
- @echo "Run \`make all-pdf' or \`make all-ps' in that directory to" \
- "run these through (pdf)latex."
-
-latexpdf:
- $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) _build/latex
- @echo "Running LaTeX files through pdflatex..."
- make -C _build/latex all-pdf
- @echo "pdflatex finished; the PDF files are in _build/latex."
-
-changes:
- $(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) $(BUILDDIR)/changes
- @echo
- @echo "The overview file is in $(BUILDDIR)/changes."
-
-linkcheck:
- $(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck
- @echo
- @echo "Link check complete; look for any errors in the above output " \
- "or in $(BUILDDIR)/linkcheck/output.txt."
-
-doctest:
- $(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest
- @echo "Testing of doctests in the sources finished, look at the " \
- "results in $(BUILDDIR)/doctest/output.txt."
+# Makefile for Sphinx documentation
+#
+
+# You can set these variables from the command line.
+SPHINXOPTS =
+SPHINXBUILD = sphinx-build
+PAPER =
+BUILDDIR = _build
+INSTALLDIR = /home/newville/public_html/lmfit/
+
+
+# Internal variables.
+PAPEROPT_a4 = -D latex_paper_size=a4
+PAPEROPT_letter = -D latex_paper_size=letter
+ALLSPHINXOPTS = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) .
+
+.PHONY: help clean html dirhtml pickle json htmlhelp qthelp latex changes linkcheck doctest latexpdf htmlzip
+.PHONY: all install pdf
+
+html:
+ cp sphinx/ext_mathjax.py extensions.py
+ $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html
+ @echo
+ @echo "html build finished: $(BUILDDIR)/html."
+
+htmlzip: html
+ cp sphinx/ext_pngmath.py extensions.py
+ $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/lmfit_doc
+ cd $(BUILDDIR) && zip -pur html/lmfit_doc.zip lmfit_doc
+
+epub:
+ cp sphinx/ext_pngmath.py extensions.py
+ $(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) $(BUILDDIR)/epub
+ cp -pr $(BUILDDIR)/epub/*.epub $(BUILDDIR)/html/.
+
+pdf: latex
+ cd $(BUILDDIR)/latex && make all-pdf
+ cp -pr $(BUILDDIR)/latex/lmfit.pdf $(BUILDDIR)/html/.
+
+all: html htmlzip epub pdf
+
+install: all
+ cd $(BUILDDIR)/latex && pdflatex lmfit.tex
+ cd $(BUILDDIR)/latex && makeindex -s python.ist lmfit.idx
+ cd $(BUILDDIR)/latex && pdflatex lmfit.tex
+ cp -pr $(BUILDDIR)/html/* $(INSTALLDIR)/.
+
+help:
+ @echo "Please use \`make <target>' where <target> is one of"
+ @echo " html to make standalone HTML files"
+ @echo " dirhtml to make HTML files named index.html in directories"
+ @echo " pickle to make pickle files"
+ @echo " json to make JSON files"
+ @echo " htmlhelp to make HTML files and a HTML help project"
+ @echo " qthelp to make HTML files and a qthelp project"
+ @echo " latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter"
+ @echo " changes to make an overview of all changed/added/deprecated items"
+ @echo " linkcheck to check all external links for integrity"
+ @echo " doctest to run all doctests embedded in the documentation (if enabled)"
+
+clean:
+ -rm -rf $(BUILDDIR)/*
+
+dirhtml:
+ $(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml
+ @echo
+ @echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml."
+
+pickle:
+ $(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle
+ @echo
+ @echo "Build finished; now you can process the pickle files."
+
+json:
+ $(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json
+ @echo
+ @echo "Build finished; now you can process the JSON files."
+
+htmlhelp:
+ $(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp
+ @echo
+ @echo "Build finished; now you can run HTML Help Workshop with the" \
+ ".hhp project file in $(BUILDDIR)/htmlhelp."
+
+latex:
+ $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) _build/latex
+ @echo
+ @echo "Build finished; the LaTeX files are in _build/latex."
+ @echo "Run \`make all-pdf' or \`make all-ps' in that directory to" \
+ "run these through (pdf)latex."
+
+latexpdf:
+ $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) _build/latex
+ @echo "Running LaTeX files through pdflatex..."
+ make -C _build/latex all-pdf
+ @echo "pdflatex finished; the PDF files are in _build/latex."
+
+changes:
+ $(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) $(BUILDDIR)/changes
+ @echo
+ @echo "The overview file is in $(BUILDDIR)/changes."
+
+linkcheck:
+ $(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck
+ @echo
+ @echo "Link check complete; look for any errors in the above output " \
+ "or in $(BUILDDIR)/linkcheck/output.txt."
+
+doctest:
+ $(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest
+ @echo "Testing of doctests in the sources finished, look at the " \
+ "results in $(BUILDDIR)/doctest/output.txt."
diff --git a/doc/__pycache__/extensions.cpython-35.pyc b/doc/__pycache__/extensions.cpython-35.pyc
new file mode 100644
index 0000000..a9f415c
Binary files /dev/null and b/doc/__pycache__/extensions.cpython-35.pyc differ
diff --git a/doc/_images/emcee_dbl_exp.png b/doc/_images/emcee_dbl_exp.png
new file mode 100644
index 0000000..11bc045
Binary files /dev/null and b/doc/_images/emcee_dbl_exp.png differ
diff --git a/doc/_images/emcee_dbl_exp2.png b/doc/_images/emcee_dbl_exp2.png
new file mode 100644
index 0000000..b2dab72
Binary files /dev/null and b/doc/_images/emcee_dbl_exp2.png differ
diff --git a/doc/_images/emcee_triangle.png b/doc/_images/emcee_triangle.png
new file mode 100644
index 0000000..3e76a52
Binary files /dev/null and b/doc/_images/emcee_triangle.png differ
diff --git a/doc/_templates/indexsidebar.html b/doc/_templates/indexsidebar.html
index 4098133..ceb1a92 100644
--- a/doc/_templates/indexsidebar.html
+++ b/doc/_templates/indexsidebar.html
@@ -1,24 +1,24 @@
-<h3>Getting LMFIT</h3>
-<p>Current version: <b>{{ release }}</b></p>
-<p>Download: <a href="http://pypi.python.org/pypi/lmfit/">PyPI (Python.org)</a>
-<p>Install: <tt>pip install lmfit</tt>
-<p>
-<p>Development version: <br>
- <a href="https://github.com/lmfit/lmfit-py/">github.com</a> <br>
-
-<h3>Questions?</h3>
-
- <a href="faq.html">Frequently Asked Questions</a><br>
- <a href="https://groups.google.com/group/lmfit-py">Mailing List</a><br>
- <a href="support.html">Getting Help</a><br>
-
-<h3>Off-line Documentation</h3>
-
-[<a href="http://cars9.uchicago.edu/software/python/lmfit/lmfit.pdf">PDF</a>
-|<a href="http://cars9.uchicago.edu/software/python/lmfit/lmfit.epub">EPUB</a>
-|<a href="http://cars9.uchicago.edu/software/python/lmfit/lmfit_doc.zip">HTML(zip)</a>
-]
-
-
-<hr>
-<p>
+<h3>Getting LMFIT</h3>
+<p>Current version: <b>{{ release }}</b></p>
+<p>Download: <a href="http://pypi.python.org/pypi/lmfit/">PyPI (Python.org)</a>
+<p>Install: <tt>pip install lmfit</tt>
+<p>
+<p>Development version: <br>
+ <a href="https://github.com/lmfit/lmfit-py/">github.com</a> <br>
+
+<h3>Questions?</h3>
+
+ <a href="faq.html">Frequently Asked Questions</a><br>
+ <a href="https://groups.google.com/group/lmfit-py">Mailing List</a><br>
+ <a href="support.html">Getting Help</a><br>
+
+<h3>Off-line Documentation</h3>
+
+[<a href="http://cars9.uchicago.edu/software/python/lmfit/lmfit.pdf">PDF</a>
+|<a href="http://cars9.uchicago.edu/software/python/lmfit/lmfit.epub">EPUB</a>
+|<a href="http://cars9.uchicago.edu/software/python/lmfit/lmfit_doc.zip">HTML(zip)</a>
+]
+
+
+<hr>
+<p>
diff --git a/doc/bounds.rst b/doc/bounds.rst
index f64ec6a..40f8390 100644
--- a/doc/bounds.rst
+++ b/doc/bounds.rst
@@ -1,79 +1,78 @@
-.. _bounds_chapter:
-
-=================================
-Bounds Implementation
-=================================
-
-.. _MINPACK-1: http://en.wikipedia.org/wiki/MINPACK
-.. _MINUIT: http://en.wikipedia.org/wiki/MINUIT
-.. _leastsqbound: https://github.com/jjhelmus/leastsqbound-scipy
-
-This section describes the implementation of :class:`Parameter` bounds.
-The `MINPACK-1`_ implementation used in :func:`scipy.optimize.leastsq` for
-the Levenberg-Marquardt algorithm does not explicitly support bounds on
-parameters, and expects to be able to fully explore the available range of
-values for any Parameter. Simply placing hard constraints (that is,
-resetting the value when it exceeds the desired bounds) prevents the
-algorithm from determining the partial derivatives, and leads to unstable
-results.
-
-Instead of placing such hard constraints, bounded parameters are
-mathematically transformed using the formulation devised (and documented)
-for `MINUIT`_. This is implemented following (and borrowing heavily from)
-the `leastsqbound`_ from J. J. Helmus. Parameter values are mapped from
-internally used, freely variable values :math:`P_{\rm internal}` to bounded
-parameters :math:`P_{\rm bounded}`. When both ``min`` and ``max`` bounds
-are specified, the mapping is
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- P_{\rm internal} &=& \arcsin\big(\frac{2 (P_{\rm bounded} - {\rm min})}{({\rm max} - {\rm min})} - 1\big) \\
- P_{\rm bounded} &=& {\rm min} + \big(\sin(P_{\rm internal}) + 1\big) \frac{({\rm max} - {\rm min})}{2}
- \end{eqnarray*}
-
-With only an upper limit ``max`` supplied, but ``min`` left unbounded, the
-mapping is:
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- P_{\rm internal} &=& \sqrt{({\rm max} - P_{\rm bounded} + 1)^2 - 1} \\
- P_{\rm bounded} &=& {\rm max} + 1 - \sqrt{P_{\rm internal}^2 + 1}
- \end{eqnarray*}
-
-With only a lower limit ``min`` supplied, but ``max`` left unbounded, the
-mapping is:
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- P_{\rm internal} &=& \sqrt{(P_{\rm bounded} - {\rm min} + 1)^2 - 1} \\
- P_{\rm bounded} &=& {\rm min} - 1 + \sqrt{P_{\rm internal}^2 + 1}
- \end{eqnarray*}
-
-With these mappings, the value for the bounded Parameter cannot exceed the
-specified bounds, though the internally varied value can be freely varied.
-
-It bears repeating that code from `leastsqbound`_ was adopted to implement
-the transformation described above. The challenging part (Thanks again to
-Jonathan J. Helmus!) here is to re-transform the covariance matrix so that
-the uncertainties can be estimated for bounded Parameters. This is
-included by using the derivate :math:`dP_{\rm internal}/dP_{\rm bounded}`
-from the equations above to re-scale the Jacobin matrix before
-constructing the covariance matrix from it. Tests show that this
-re-scaling of the covariance matrix works quite well, and that
-uncertainties estimated for bounded are quite reasonable. Of course, if
-the best fit value is very close to a boundary, the derivative estimated
-uncertainty and correlations for that parameter may not be reliable.
-
-The `MINUIT`_ documentation recommends caution in using bounds. Setting
-bounds can certainly increase the number of function evaluations (and so
-computation time), and in some cases may cause some instabilities, as the
-range of acceptable parameter values is not fully explored. On the other
-hand, preliminary tests suggest that using ``max`` and ``min`` to set
-clearly outlandish bounds does not greatly affect performance or results.
-
+.. _bounds_chapter:
+
+=================================
+Bounds Implementation
+=================================
+
+.. _MINPACK-1: http://en.wikipedia.org/wiki/MINPACK
+.. _MINUIT: http://en.wikipedia.org/wiki/MINUIT
+.. _leastsqbound: https://github.com/jjhelmus/leastsqbound-scipy
+
+This section describes the implementation of :class:`Parameter` bounds.
+The `MINPACK-1`_ implementation used in :scipydoc:`optimize.leastsq` for
+the Levenberg-Marquardt algorithm does not explicitly support bounds on
+parameters, and expects to be able to fully explore the available range of
+values for any Parameter. Simply placing hard constraints (that is,
+resetting the value when it exceeds the desired bounds) prevents the
+algorithm from determining the partial derivatives, and leads to unstable
+results.
+
+Instead of placing such hard constraints, bounded parameters are
+mathematically transformed using the formulation devised (and documented)
+for `MINUIT`_. This is implemented following (and borrowing heavily from)
+the `leastsqbound`_ from J. J. Helmus. Parameter values are mapped from
+internally used, freely variable values :math:`P_{\rm internal}` to bounded
+parameters :math:`P_{\rm bounded}`. When both ``min`` and ``max`` bounds
+are specified, the mapping is
+
+.. math::
+ :nowrap:
+
+ \begin{eqnarray*}
+ P_{\rm internal} &=& \arcsin\big(\frac{2 (P_{\rm bounded} - {\rm min})}{({\rm max} - {\rm min})} - 1\big) \\
+ P_{\rm bounded} &=& {\rm min} + \big(\sin(P_{\rm internal}) + 1\big) \frac{({\rm max} - {\rm min})}{2}
+ \end{eqnarray*}
+
+With only an upper limit ``max`` supplied, but ``min`` left unbounded, the
+mapping is:
+
+.. math::
+ :nowrap:
+
+ \begin{eqnarray*}
+ P_{\rm internal} &=& \sqrt{({\rm max} - P_{\rm bounded} + 1)^2 - 1} \\
+ P_{\rm bounded} &=& {\rm max} + 1 - \sqrt{P_{\rm internal}^2 + 1}
+ \end{eqnarray*}
+
+With only a lower limit ``min`` supplied, but ``max`` left unbounded, the
+mapping is:
+
+.. math::
+ :nowrap:
+
+ \begin{eqnarray*}
+ P_{\rm internal} &=& \sqrt{(P_{\rm bounded} - {\rm min} + 1)^2 - 1} \\
+ P_{\rm bounded} &=& {\rm min} - 1 + \sqrt{P_{\rm internal}^2 + 1}
+ \end{eqnarray*}
+
+With these mappings, the value for the bounded Parameter cannot exceed the
+specified bounds, though the internally varied value can be freely varied.
+
+It bears repeating that code from `leastsqbound`_ was adopted to implement
+the transformation described above. The challenging part (Thanks again to
+Jonathan J. Helmus!) here is to re-transform the covariance matrix so that
+the uncertainties can be estimated for bounded Parameters. This is
+included by using the derivate :math:`dP_{\rm internal}/dP_{\rm bounded}`
+from the equations above to re-scale the Jacobin matrix before
+constructing the covariance matrix from it. Tests show that this
+re-scaling of the covariance matrix works quite well, and that
+uncertainties estimated for bounded are quite reasonable. Of course, if
+the best fit value is very close to a boundary, the derivative estimated
+uncertainty and correlations for that parameter may not be reliable.
+
+The `MINUIT`_ documentation recommends caution in using bounds. Setting
+bounds can certainly increase the number of function evaluations (and so
+computation time), and in some cases may cause some instabilities, as the
+range of acceptable parameter values is not fully explored. On the other
+hand, preliminary tests suggest that using ``max`` and ``min`` to set
+clearly outlandish bounds does not greatly affect performance or results.
diff --git a/doc/builtin_models.rst b/doc/builtin_models.rst
index 9d2671e..d1e68b6 100644
--- a/doc/builtin_models.rst
+++ b/doc/builtin_models.rst
@@ -1,943 +1,980 @@
-.. _builtin_models_chapter:
-
-=====================================================
-Built-in Fitting Models in the :mod:`models` module
-=====================================================
-
-.. module:: models
-
-Lmfit provides several builtin fitting models in the :mod:`models` module.
-These pre-defined models each subclass from the :class:`model.Model` class of the
-previous chapter and wrap relatively well-known functional forms, such as
-Gaussians, Lorentzian, and Exponentials that are used in a wide range of
-scientific domains. In fact, all the models are all based on simple, plain
-python functions defined in the :mod:`lineshapes` module. In addition to
-wrapping a function into a :class:`model.Model`, these models also provide a
-:meth:`guess` method that is intended to give a reasonable
-set of starting values from a data array that closely approximates the
-data to be fit.
-
-As shown in the previous chapter, a key feature of the :class:`mode.Model` class
-is that models can easily be combined to give a composite
-:class:`model.Model`. Thus while some of the models listed here may seem pretty
-trivial (notably, :class:`ConstantModel` and :class:`LinearModel`), the
-main point of having these is to be able to used in composite models. For
-example, a Lorentzian plus a linear background might be represented as::
-
- >>> from lmfit.models import LinearModel, LorentzianModel
- >>> peak = LorentzianModel()
- >>> background = LinearModel()
- >>> model = peak + background
-
-All the models listed below are one dimensional, with an independent
-variable named ``x``. Many of these models represent a function with a
-distinct peak, and so share common features. To maintain uniformity,
-common parameter names are used whenever possible. Thus, most models have
-a parameter called ``amplitude`` that represents the overall height (or
-area of) a peak or function, a ``center`` parameter that represents a peak
-centroid position, and a ``sigma`` parameter that gives a characteristic
-width. Some peak shapes also have a parameter ``fwhm``, typically
-constrained by ``sigma`` to give the full width at half maximum.
-
-After a list of builtin models, a few examples of their use is given.
-
-Peak-like models
--------------------
-
-There are many peak-like models available. These include
-:class:`GaussianModel`, :class:`LorentzianModel`, :class:`VoigtModel` and
-some less commonly used variations. The :meth:`guess`
-methods for all of these make a fairly crude guess for the value of
-``amplitude``, but also set a lower bound of 0 on the value of ``sigma``.
-
-:class:`GaussianModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: GaussianModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Gaussian or normal distribution lineshape
-<http://en.wikipedia.org/wiki/Normal_distribution>`_. Parameter names:
-``amplitude``, ``center``, and ``sigma``. In addition, a constrained
-parameter ``fwhm`` is included.
-
-.. math::
-
- f(x; A, \mu, \sigma) = \frac{A}{\sigma\sqrt{2\pi}} e^{[{-{(x-\mu)^2}/{{2\sigma}^2}}]}
-
-where the parameter ``amplitude`` corresponds to :math:`A`, ``center`` to
-:math:`\mu`, and ``sigma`` to :math:`\sigma`. The full width at
-half maximum is :math:`2\sigma\sqrt{2\ln{2}}`, approximately
-:math:`2.3548\sigma`
-
-
-:class:`LorentzianModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: LorentzianModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Lorentzian or Cauchy-Lorentz distribution function
-<http://en.wikipedia.org/wiki/Cauchy_distribution>`_. Parameter names:
-``amplitude``, ``center``, and ``sigma``. In addition, a constrained
-parameter ``fwhm`` is included.
-
-.. math::
-
- f(x; A, \mu, \sigma) = \frac{A}{\pi} \big[\frac{\sigma}{(x - \mu)^2 + \sigma^2}\big]
-
-where the parameter ``amplitude`` corresponds to :math:`A`, ``center`` to
-:math:`\mu`, and ``sigma`` to :math:`\sigma`. The full width at
-half maximum is :math:`2\sigma`.
-
-
-:class:`VoigtModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: VoigtModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Voigt distribution function
-<http://en.wikipedia.org/wiki/Voigt_profile>`_. Parameter names:
-``amplitude``, ``center``, and ``sigma``. A ``gamma`` parameter is also
-available. By default, it is constrained to have value equal to ``sigma``,
-though this can be varied independently. In addition, a constrained
-parameter ``fwhm`` is included. The definition for the Voigt function used
-here is
-
-.. math::
-
- f(x; A, \mu, \sigma, \gamma) = \frac{A \textrm{Re}[w(z)]}{\sigma\sqrt{2 \pi}}
-
-where
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- z &=& \frac{x-\mu +i\gamma}{\sigma\sqrt{2}} \\
- w(z) &=& e^{-z^2}{\operatorname{erfc}}(-iz)
- \end{eqnarray*}
-
-and :func:`erfc` is the complimentary error function. As above,
-``amplitude`` corresponds to :math:`A`, ``center`` to
-:math:`\mu`, and ``sigma`` to :math:`\sigma`. The parameter ``gamma``
-corresponds to :math:`\gamma`.
-If ``gamma`` is kept at the default value (constrained to ``sigma``),
-the full width at half maximum is approximately :math:`3.6013\sigma`.
-
-
-:class:`PseudoVoigtModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: PseudoVoigtModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-a model based on a `pseudo-Voigt distribution function
-<http://en.wikipedia.org/wiki/Voigt_profile#Pseudo-Voigt_Approximation>`_,
-which is a weighted sum of a Gaussian and Lorentzian distribution functions
-with that share values for ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`)
-and full width at half maximum (and so have constrained values of
-``sigma`` (:math:`\sigma`). A parameter ``fraction`` (:math:`\alpha`)
-controls the relative weight of the Gaussian and Lorentzian components,
-giving the full definition of
-
-.. math::
-
- f(x; A, \mu, \sigma, \alpha) = \frac{(1-\alpha)A}{\sigma_g\sqrt{2\pi}} e^{[{-{(x-\mu)^2}/{{2\sigma_g}^2}}]}
- + \frac{\alpha A}{\pi} \big[\frac{\sigma}{(x - \mu)^2 + \sigma^2}\big]
-
-where :math:`\sigma_g = {\sigma}/{\sqrt{2\ln{2}}}` so that the full width
-at half maximum of each component and of the sum is :math:`2\sigma`. The
-:meth:`guess` function always sets the starting value for ``fraction`` at 0.5.
-
-
-:class:`MoffatModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: MoffatModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-a model based on a `Moffat distribution function
-<https://en.wikipedia.org/wiki/Moffat_distribution>`_, the parameters are
-``amplitude`` (:math:`A`), ``center`` (:math:`\mu`),
-a width parameter ``sigma`` (:math:`\sigma`) and an exponent ``beta`` (:math:`\beta`).
-For (:math:`\beta=1`) the Moffat has a Lorentzian shape.
-
-.. math::
-
- f(x; A, \mu, \sigma, \beta) = A \big[(\frac{x-\mu}{\sigma})^2+1\big]^{-\beta}
-
-the full width have maximum is :math:`2\sigma\sqrt{2^{1/\beta}-1}`.
-:meth:`guess` function always sets the starting value for ``beta`` to 1.
-
-
-:class:`Pearson7Model`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: Pearson7Model(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Pearson VII distribution
-<http://en.wikipedia.org/wiki/Pearson_distribution#The_Pearson_type_VII_distribution>`_.
-This is a Lorenztian-like distribution function. It has the usual
-parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
-``sigma`` (:math:`\sigma`), and also an ``exponent`` (:math:`m`) in
-
-.. math::
-
- f(x; A, \mu, \sigma, m) = \frac{A}{\sigma{\beta(m-\frac{1}{2}, \frac{1}{2})}} \bigl[1 + \frac{(x-\mu)^2}{\sigma^2} \bigr]^{-m}
-
-where :math:`\beta` is the beta function (see :func:`scipy.special.beta` in
-:mod:`scipy.special`). The :meth:`guess` function always
-gives a starting value for ``exponent`` of 1.5.
-
-:class:`StudentsTModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: StudentsTModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Student's t distribution function
-<http://en.wikipedia.org/wiki/Student%27s_t-distribution>`_, with the usual
-parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
-``sigma`` (:math:`\sigma`) in
-
-.. math::
-
- f(x; A, \mu, \sigma) = \frac{A \Gamma(\frac{\sigma+1}{2})} {\sqrt{\sigma\pi}\,\Gamma(\frac{\sigma}{2})} \Bigl[1+\frac{(x-\mu)^2}{\sigma}\Bigr]^{-\frac{\sigma+1}{2}}
-
-
-where :math:`\Gamma(x)` is the gamma function.
-
-
-:class:`BreitWignerModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: BreitWignerModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Breit-Wigner-Fano function
-<http://en.wikipedia.org/wiki/Fano_resonance>`_. It has the usual
-parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
-``sigma`` (:math:`\sigma`), plus ``q`` (:math:`q`) in
-
-.. math::
-
- f(x; A, \mu, \sigma, q) = \frac{A (q\sigma/2 + x - \mu)^2}{(\sigma/2)^2 + (x - \mu)^2}
-
-
-:class:`LognormalModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: LognormalModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on the `Log-normal distribution function
-<http://en.wikipedia.org/wiki/Lognormal>`_.
-It has the usual parameters
-``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and ``sigma``
-(:math:`\sigma`) in
-
-.. math::
-
- f(x; A, \mu, \sigma) = \frac{A e^{-(\ln(x) - \mu)/ 2\sigma^2}}{x}
-
-
-:class:`DampedOcsillatorModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: DampedOcsillatorModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on the `Damped Harmonic Oscillator Amplitude
-<http://en.wikipedia.org/wiki/Harmonic_oscillator#Amplitude_part>`_.
-It has the usual parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
-``sigma`` (:math:`\sigma`) in
-
-.. math::
-
- f(x; A, \mu, \sigma) = \frac{A}{\sqrt{ [1 - (x/\mu)^2]^2 + (2\sigma x/\mu)^2}}
-
-
-:class:`ExponentialGaussianModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: ExponentialGaussianModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model of an `Exponentially modified Gaussian distribution
-<http://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution>`_.
-It has the usual parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
-``sigma`` (:math:`\sigma`), and also ``gamma`` (:math:`\gamma`) in
-
-.. math::
-
- f(x; A, \mu, \sigma, \gamma) = \frac{A\gamma}{2}
- \exp\bigl[\gamma({\mu - x + \gamma\sigma^2/2})\bigr]
- {\operatorname{erfc}}\Bigl(\frac{\mu + \gamma\sigma^2 - x}{\sqrt{2}\sigma}\Bigr)
-
-
-where :func:`erfc` is the complimentary error function.
-
-:class:`SkewedGaussianModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: SkewedGaussianModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A variation of the above model, this is a `Skewed normal distribution
-<http://en.wikipedia.org/wiki/Skew_normal_distribution>`_.
-It has the usual parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
-``sigma`` (:math:`\sigma`), and also ``gamma`` (:math:`\gamma`) in
-
-.. math::
-
- f(x; A, \mu, \sigma, \gamma) = \frac{A}{\sigma\sqrt{2\pi}}
- e^{[{-{(x-\mu)^2}/{{2\sigma}^2}}]} \Bigl\{ 1 +
- {\operatorname{erf}}\bigl[
- \frac{\gamma(x-\mu)}{\sigma\sqrt{2}}
- \bigr] \Bigr\}
-
-
-where :func:`erf` is the error function.
-
-
-:class:`DonaichModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: DonaichModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model of an `Doniach Sunjic asymmetric lineshape
-<http://www.casaxps.com/help_manual/line_shapes.htm>`_, used in
-photo-emission. With the usual parameters ``amplitude`` (:math:`A`),
-``center`` (:math:`\mu`) and ``sigma`` (:math:`\sigma`), and also ``gamma``
-(:math:`\gamma`) in
-
-.. math::
-
- f(x; A, \mu, \sigma, \gamma) = A\frac{\cos\bigl[\pi\gamma/2 + (1-\gamma)
- \arctan{(x - \mu)}/\sigma\bigr]} {\bigr[1 + (x-\mu)/\sigma\bigl]^{(1-\gamma)/2}}
-
-
-Linear and Polynomial Models
-------------------------------------
-
-These models correspond to polynomials of some degree. Of course, lmfit is
-a very inefficient way to do linear regression (see :func:`numpy.polyfit`
-or :func:`scipy.stats.linregress`), but these models may be useful as one
-of many components of composite model.
-
-:class:`ConstantModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: ConstantModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
- a class that consists of a single value, ``c``. This is constant in the
- sense of having no dependence on the independent variable ``x``, not in
- the sense of being non-varying. To be clear, ``c`` will be a variable
- Parameter.
-
-:class:`LinearModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: LinearModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
- a class that gives a linear model:
-
-.. math::
-
- f(x; m, b) = m x + b
-
-with parameters ``slope`` for :math:`m` and ``intercept`` for :math:`b`.
-
-
-:class:`QuadraticModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: QuadraticModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-
- a class that gives a quadratic model:
-
-.. math::
-
- f(x; a, b, c) = a x^2 + b x + c
-
-with parameters ``a``, ``b``, and ``c``.
-
-
-:class:`ParabolicModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: ParabolicModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
- same as :class:`QuadraticModel`.
-
-
-:class:`PolynomialModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-
-.. class:: PolynomialModel(degree, missing=None[, prefix=''[, name=None[, **kws]]])
-
- a class that gives a polynomial model up to ``degree`` (with maximum
- value of 7).
-
-.. math::
-
- f(x; c_0, c_1, \ldots, c_7) = \sum_{i=0, 7} c_i x^i
-
-with parameters ``c0``, ``c1``, ..., ``c7``. The supplied ``degree``
-will specify how many of these are actual variable parameters. This uses
-:func:`numpy.polyval` for its calculation of the polynomial.
-
-
-
-Step-like models
------------------------------------------------
-
-Two models represent step-like functions, and share many characteristics.
-
-:class:`StepModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: StepModel(form='linear'[, missing=None[, prefix=''[, name=None[, **kws]]]])
-
-A model based on a Step function, with four choices for functional form.
-The step function starts with a value 0, and ends with a value of :math:`A`
-(``amplitude``), rising to :math:`A/2` at :math:`\mu` (``center``),
-with :math:`\sigma` (``sigma``) setting the characteristic width. The
-supported functional forms are ``linear`` (the default), ``atan`` or
-``arctan`` for an arc-tangent function, ``erf`` for an error function, or
-``logistic`` for a `logistic function <http://en.wikipedia.org/wiki/Logistic_function>`_.
-The forms are
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- & f(x; A, \mu, \sigma, {\mathrm{form={}'linear{}'}}) & = A \min{[1, \max{(0, \alpha)}]} \\
- & f(x; A, \mu, \sigma, {\mathrm{form={}'arctan{}'}}) & = A [1/2 + \arctan{(\alpha)}/{\pi}] \\
- & f(x; A, \mu, \sigma, {\mathrm{form={}'erf{}'}}) & = A [1 + {\operatorname{erf}}(\alpha)]/2 \\
- & f(x; A, \mu, \sigma, {\mathrm{form={}'logistic{}'}})& = A [1 - \frac{1}{1 + e^{\alpha}} ]
- \end{eqnarray*}
-
-where :math:`\alpha = (x - \mu)/{\sigma}`.
-
-:class:`RectangleModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-
-.. class:: RectangleModel(form='linear'[, missing=None[, prefix=''[, name=None[, **kws]]]])
-
-A model based on a Step-up and Step-down function of the same form. The
-same choices for functional form as for :class:`StepModel` are supported,
-with ``linear`` as the default. The function starts with a value 0, and
-ends with a value of :math:`A` (``amplitude``), rising to :math:`A/2` at
-:math:`\mu_1` (``center1``), with :math:`\sigma_1` (``sigma1``) setting the
-characteristic width. It drops to rising to :math:`A/2` at :math:`\mu_2`
-(``center2``), with characteristic width :math:`\sigma_2` (``sigma2``).
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- &f(x; A, \mu, \sigma, {\mathrm{form={}'linear{}'}}) &= A \{ \min{[1, \max{(0, \alpha_1)}]} + \min{[-1, \max{(0, \alpha_2)}]} \} \\
- &f(x; A, \mu, \sigma, {\mathrm{form={}'arctan{}'}}) &= A [\arctan{(\alpha_1)} + \arctan{(\alpha_2)}]/{\pi} \\
- &f(x; A, \mu, \sigma, {\mathrm{form={}'erf{}'}}) &= A [{\operatorname{erf}}(\alpha_1) + {\operatorname{erf}}(\alpha_2)]/2 \\
- &f(x; A, \mu, \sigma, {\mathrm{form={}'logistic{}'}}) &= A [1 - \frac{1}{1 + e^{\alpha_1}} - \frac{1}{1 + e^{\alpha_2}} ]
- \end{eqnarray*}
-
-
-where :math:`\alpha_1 = (x - \mu_1)/{\sigma_1}` and :math:`\alpha_2 = -(x - \mu_2)/{\sigma_2}`.
-
-
-Exponential and Power law models
------------------------------------------------
-
-:class:`ExponentialModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: ExponentialModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on an `exponential decay function
-<http://en.wikipedia.org/wiki/Exponential_decay>`_. With parameters named
-``amplitude`` (:math:`A`), and ``decay`` (:math:`\tau`), this has the form:
-
-.. math::
-
- f(x; A, \tau) = A e^{-x/\tau}
-
-
-:class:`PowerLawModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: PowerLawModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Power Law <http://en.wikipedia.org/wiki/Power_law>`_.
-With parameters
-named ``amplitude`` (:math:`A`), and ``exponent`` (:math:`k`), this has the
-form:
-
-.. math::
-
- f(x; A, k) = A x^k
-
-
-User-defined Models
-----------------------------
-
-.. _asteval: http://newville.github.io/asteval/
-
-As shown in the previous chapter (:ref:`model_chapter`), it is fairly
-straightforward to build fitting models from parametrized python functions.
-The number of model classes listed so far in the present chapter should
-make it clear that this process is not too difficult. Still, it is
-sometimes desirable to build models from a user-supplied function. This
-may be especially true if model-building is built-in to some larger library
-or application for fitting in which the user may not be able to easily
-build and use a new model from python code.
-
-
-The :class:`ExpressionModel` allows a model to be built from a
-user-supplied expression. This uses the `asteval`_ module also used for
-mathematical constraints as discussed in :ref:`constraints_chapter`.
-
-
-:class:`ExpressionModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: ExpressionModel(expr, independent_vars=None, init_script=None, **kws)
-
- A model using the user-supplied mathematical expression, which can be nearly any valid Python expresion.
-
- :param expr: expression use to build model
- :type expr: string
- :param independent_vars: list of argument names in expression that are independent variables.
- :type independent_vars: ``None`` (default) or list of strings for independent variables.
- :param init_script: python script to run before parsing and evaluating expression.
- :type init_script: ``None`` (default) or string
-
-with other parameters passed to :class:`model.Model`, with the notable
-exception that :class:`ExpressionModel` does **not** support the `prefix` argument.
-
-Since the point of this model is that an arbitrary expression will be
-supplied, the determination of what are the parameter names for the model
-happens when the model is created. To do this, the expression is parsed,
-and all symbol names are found. Names that are already known (there are
-over 500 function and value names in the asteval namespace, including most
-python builtins, more than 200 functions inherited from numpy, and more
-than 20 common lineshapes defined in the :mod:`lineshapes` module) are not
-converted to parameters. Unrecognized name are expected to be names either
-of parameters or independent variables. If `independent_vars` is the
-default value of ``None``, and if the expression contains a variable named
-`x`, that will be used as the independent variable. Otherwise,
-`independent_vars` must be given.
-
-For example, if one creates an :class:`ExpressionModel` as::
-
- >>> mod = ExpressionModel('off + amp * exp(-x/x0) * sin(x*phase)')
-
-The name `exp` will be recognized as the exponent function, so the model
-will be interpreted to have parameters named `off`, `amp`, `x0` and
-`phase`. In addition, `x` will be assumed to be the sole independent variable.
-In general, there is no obvious way to set default parameter values or
-parameter hints for bounds, so this will have to be handled explicitly.
-
-To evaluate this model, you might do the following::
-
- >>> x = numpy.linspace(0, 10, 501)
- >>> params = mod.make_params(off=0.25, amp=1.0, x0=2.0, phase=0.04)
- >>> y = mod.eval(params, x=x)
-
-
-While many custom models can be built with a single line expression
-(especially since the names of the lineshapes like `gaussian`, `lorentzian`
-and so on, as well as many numpy functions, are available), more complex
-models will inevitably require multiple line functions. You can include
-such Python code with the `init_script` argument. The text of this script
-is evaluated when the model is initialized (and before the actual
-expression is parsed), so that you can define functions to be used
-in your expression.
-
-As a probably unphysical example, to make a model that is the derivative of
-a Gaussian function times the logarithm of a Lorentzian function you may
-could to define this in a script::
-
- >>> script = """
- def mycurve(x, amp, cen, sig):
- loren = lorentzian(x, amplitude=amp, center=cen, sigma=sig)
- gauss = gaussian(x, amplitude=amp, center=cen, sigma=sig)
- return log(loren)*gradient(gauss)/gradient(x)
- """
-
-and then use this with :class:`ExpressionModel` as::
-
- >>> mod = ExpressionModel('mycurve(x, height, mid, wid)',
- init_script=script,
- independent_vars=['x'])
-
-As above, this will interpret the parameter names to be `height`, `mid`,
-and `wid`, and build a model that can be used to fit data.
-
-
-
-Example 1: Fit Peaked data to Gaussian, Lorentzian, and Voigt profiles
-------------------------------------------------------------------------
-
-Here, we will fit data to three similar line shapes, in order to decide which
-might be the better model. We will start with a Gaussian profile, as in
-the previous chapter, but use the built-in :class:`GaussianModel` instead
-of one we write ourselves. This is a slightly different version from the
-one in previous example in that the parameter names are different, and have
-built-in default values. So, we'll simply use::
-
- from numpy import loadtxt
- from lmfit.models import GaussianModel
-
- data = loadtxt('test_peak.dat')
- x = data[:, 0]
- y = data[:, 1]
-
- mod = GaussianModel()
- pars = mod.guess(y, x=x)
- out = mod.fit(y, pars, x=x)
- print(out.fit_report(min_correl=0.25))
-
-which prints out the results::
-
- [[Model]]
- gaussian
- [[Fit Statistics]]
- # function evals = 21
- # data points = 401
- # variables = 3
- chi-square = 29.994
- reduced chi-square = 0.075
- [[Variables]]
- amplitude: 30.3135571 +/- 0.157126 (0.52%) (init= 29.08159)
- center: 9.24277049 +/- 0.007374 (0.08%) (init= 9.25)
- fwhm: 2.90156963 +/- 0.017366 (0.60%) == '2.3548200*sigma'
- sigma: 1.23218319 +/- 0.007374 (0.60%) (init= 1.35)
- [[Correlations]] (unreported correlations are < 0.250)
- C(amplitude, sigma) = 0.577
-
-
-[We see a few interesting differences from the results of the previous
- chapter. First, the parameter names are longer. Second, there is a
- ``fwhm`` parameter, defined as :math:`\sim 2.355\sigma`. And third, the
- automated initial guesses are pretty good. A plot of the fit shows not
- such a great fit:
-
-.. _figA1:
-
- .. image:: _images/models_peak1.png
- :target: _images/models_peak1.png
- :width: 48 %
- .. image:: _images/models_peak2.png
- :target: _images/models_peak2.png
- :width: 48 %
-
- Fit to peak with Gaussian (left) and Lorentzian (right) models.
-
-suggesting that a different peak shape, with longer tails, should be used.
-Perhaps a Lorentzian would be better? To do this, we simply replace
-``GaussianModel`` with ``LorentzianModel`` to get a
-:class:`LorentzianModel`::
-
- from lmfit.models import LorentzianModel
- mod = LorentzianModel()
- pars = mod.guess(y, x=x)
- out = mod.fit(y, pars, x=x)
- print(out.fit_report(min_correl=0.25))
-
-Predictably, the first thing we try gives results that are worse::
-
- [[Model]]
- lorentzian
- [[Fit Statistics]]
- # function evals = 25
- # data points = 401
- # variables = 3
- chi-square = 53.754
- reduced chi-square = 0.135
- [[Variables]]
- amplitude: 38.9728645 +/- 0.313857 (0.81%) (init= 36.35199)
- center: 9.24438944 +/- 0.009275 (0.10%) (init= 9.25)
- fwhm: 2.30969034 +/- 0.026312 (1.14%) == '2.0000000*sigma'
- sigma: 1.15484517 +/- 0.013156 (1.14%) (init= 1.35)
- [[Correlations]] (unreported correlations are < 0.250)
- C(amplitude, sigma) = 0.709
-
-
-with the plot shown on the right in the figure above.
-
-A Voigt model does a better job. Using :class:`VoigtModel`, this is
-as simple as::
-
- from lmfit.models import VoigtModel
- mod = VoigtModel()
- pars = mod.guess(y, x=x)
- out = mod.fit(y, pars, x=x)
- print(out.fit_report(min_correl=0.25))
-
-which gives::
-
- [[Model]]
- voigt
- [[Fit Statistics]]
- # function evals = 17
- # data points = 401
- # variables = 3
- chi-square = 14.545
- reduced chi-square = 0.037
- [[Variables]]
- amplitude: 35.7554017 +/- 0.138614 (0.39%) (init= 43.62238)
- center: 9.24411142 +/- 0.005054 (0.05%) (init= 9.25)
- fwhm: 2.62951718 +/- 0.013269 (0.50%) == '3.6013100*sigma'
- gamma: 0.73015574 +/- 0.003684 (0.50%) == 'sigma'
- sigma: 0.73015574 +/- 0.003684 (0.50%) (init= 0.8775)
- [[Correlations]] (unreported correlations are < 0.250)
- C(amplitude, sigma) = 0.651
-
-
-with the much better value for :math:`\chi^2` and the obviously better
-match to the data as seen in the figure below (left).
-
-.. _figA2:
-
- .. image:: _images/models_peak3.png
- :target: _images/models_peak3.png
- :width: 48 %
- .. image:: _images/models_peak4.png
- :target: _images/models_peak4.png
- :width: 48 %
-
- Fit to peak with Voigt model (left) and Voigt model with ``gamma``
- varying independently of ``sigma`` (right).
-
-The Voigt function has a :math:`\gamma` parameter (``gamma``) that can be
-distinct from ``sigma``. The default behavior used above constrains
-``gamma`` to have exactly the same value as ``sigma``. If we allow these
-to vary separately, does the fit improve? To do this, we have to change
-the ``gamma`` parameter from a constrained expression and give it a
-starting value::
-
- mod = VoigtModel()
- pars = mod.guess(y, x=x)
- pars['gamma'].set(value=0.7, vary=True, expr='')
-
- out = mod.fit(y, pars, x=x)
- print(out.fit_report(min_correl=0.25))
-
-which gives::
-
- [[Model]]
- voigt
- [[Fit Statistics]]
- # function evals = 21
- # data points = 401
- # variables = 4
- chi-square = 10.930
- reduced chi-square = 0.028
- [[Variables]]
- amplitude: 34.1914716 +/- 0.179468 (0.52%) (init= 43.62238)
- center: 9.24374845 +/- 0.004419 (0.05%) (init= 9.25)
- fwhm: 3.22385491 +/- 0.050974 (1.58%) == '3.6013100*sigma'
- gamma: 0.52540157 +/- 0.018579 (3.54%) (init= 0.7)
- sigma: 0.89518950 +/- 0.014154 (1.58%) (init= 0.8775)
- [[Correlations]] (unreported correlations are < 0.250)
- C(amplitude, gamma) = 0.821
-
-
-and the fit shown on the right above.
-
-Comparing the two fits with the Voigt function, we see that :math:`\chi^2`
-is definitely improved with a separately varying ``gamma`` parameter. In
-addition, the two values for ``gamma`` and ``sigma`` differ significantly
--- well outside the estimated uncertainties. Even more compelling, reduced
-:math:`\chi^2` is improved even though a fourth variable has been added to
-the fit. In the simplest statistical sense, this suggests that ``gamma``
-is a significant variable in the model.
-
-
-This example shows how easy it can be to alter and compare fitting models
-for simple problems. The example is included in the ``doc_peakmodels.py``
-file in the examples directory.
-
-
-Example 2: Fit data to a Composite Model with pre-defined models
-------------------------------------------------------------------
-
-Here, we repeat the point made at the end of the last chapter that
-instances of :class:`model.Model` class can be added together to make a
-*composite model*. By using the large number of built-in models available,
-it is therefore very simple to build models that contain multiple peaks and
-various backgrounds. An example of a simple fit to a noisy step function
-plus a constant:
-
-.. literalinclude:: ../examples/doc_stepmodel.py
-
-After constructing step-like data, we first create a :class:`StepModel`
-telling it to use the ``erf`` form (see details above), and a
-:class:`ConstantModel`. We set initial values, in one case using the data
-and :meth:`guess` method for the initial step function paramaters, and
-:meth:`make_params` arguments for the linear component.
-After making a composite model, we run :meth:`fit` and report the
-results, which give::
-
-
- [[Model]]
- Composite Model:
- step(prefix='step_',form='erf')
- linear(prefix='line_')
- [[Fit Statistics]]
- # function evals = 49
- # data points = 201
- # variables = 5
- chi-square = 633.465
- reduced chi-square = 3.232
- [[Variables]]
- line_intercept: 11.5685248 +/- 0.285611 (2.47%) (init= 10.72406)
- line_slope: 2.03270159 +/- 0.096041 (4.72%) (init= 0)
- step_amplitude: 112.270535 +/- 0.674790 (0.60%) (init= 136.3006)
- step_center: 3.12343845 +/- 0.005370 (0.17%) (init= 2.5)
- step_sigma: 0.67468813 +/- 0.011336 (1.68%) (init= 1.428571)
- [[Correlations]] (unreported correlations are < 0.100)
- C(step_amplitude, step_sigma) = 0.564
- C(line_intercept, step_center) = 0.428
- C(step_amplitude, step_center) = 0.109
-
-with a plot of
-
-.. image:: _images/models_stepfit.png
- :target: _images/models_stepfit.png
- :width: 50 %
-
-
-Example 3: Fitting Multiple Peaks -- and using Prefixes
-------------------------------------------------------------------
-
-.. _NIST StRD: http://itl.nist.gov/div898/strd/nls/nls_main.shtml
-
-As shown above, many of the models have similar parameter names. For
-composite models, this could lead to a problem of having parameters for
-different parts of the model having the same name. To overcome this, each
-:class:`model.Model` can have a ``prefix`` attribute (normally set to a blank
-string) that will be put at the beginning of each parameter name. To
-illustrate, we fit one of the classic datasets from the `NIST StRD`_ suite
-involving a decaying exponential and two gaussians.
-
-.. literalinclude:: ../examples/doc_nistgauss.py
-
-
-where we give a separate prefix to each model (they all have an
-``amplitude`` parameter). The ``prefix`` values are attached transparently
-to the models.
-
-MN----: Note that the calls to :meth:`make_param` used the bare
-name, without the prefix. We could have used them, but because we used the
-individual model ``gauss1`` and ``gauss2``, there was no need.
-
-
-Note also in the example here that we explicitly set bounds on many of the
-parameter values.
-
-The fit results printed out are::
-
- [[Model]]
- Composite Model:
- gaussian(prefix='g1_')
- gaussian(prefix='g2_')
- exponential(prefix='exp_')
- [[Fit Statistics]]
- # function evals = 55
- # data points = 250
- # variables = 8
- chi-square = 1247.528
- reduced chi-square = 5.155
- [[Variables]]
- exp_amplitude: 99.0183291 +/- 0.537487 (0.54%) (init= 162.2102)
- exp_decay: 90.9508788 +/- 1.103104 (1.21%) (init= 93.24905)
- g1_amplitude: 4257.77384 +/- 42.38354 (1.00%) (init= 2000)
- g1_center: 107.030955 +/- 0.150068 (0.14%) (init= 105)
- g1_fwhm: 39.2609205 +/- 0.377907 (0.96%) == '2.3548200*g1_sigma'
- g1_sigma: 16.6725781 +/- 0.160482 (0.96%) (init= 15)
- g2_amplitude: 2493.41747 +/- 36.16907 (1.45%) (init= 2000)
- g2_center: 153.270103 +/- 0.194665 (0.13%) (init= 155)
- g2_fwhm: 32.5128760 +/- 0.439860 (1.35%) == '2.3548200*g2_sigma'
- g2_sigma: 13.8069474 +/- 0.186791 (1.35%) (init= 15)
- [[Correlations]] (unreported correlations are < 0.500)
- C(g1_amplitude, g1_sigma) = 0.824
- C(g2_amplitude, g2_sigma) = 0.815
- C(g1_sigma, g2_center) = 0.684
- C(g1_amplitude, g2_center) = 0.648
- C(g1_center, g2_center) = 0.621
- C(g1_center, g1_sigma) = 0.507
-
-
-
-We get a very good fit to this challenging problem (described at the NIST
-site as of average difficulty, but the tests there are generally hard) by
-applying reasonable initial guesses and putting modest but explicit bounds
-on the parameter values. This fit is shown on the left:
-
-.. _figA3:
-
- .. image:: _images/models_nistgauss.png
- :target: _images/models_nistgauss.png
- :width: 48 %
- .. image:: _images/models_nistgauss2.png
- :target: _images/models_nistgauss2.png
- :width: 48 %
-
-
-One final point on setting initial values. From looking at the data
-itself, we can see the two Gaussian peaks are reasonably well separated but
-do overlap. Furthermore, we can tell that the initial guess for the
-decaying exponential component was poorly estimated because we used the
-full data range. We can simplify the initial parameter values by using
-this, and by defining an :func:`index_of` function to limit the data range.
-That is, with::
-
- def index_of(arrval, value):
- "return index of array *at or below* value "
- if value < min(arrval): return 0
- return max(np.where(arrval<=value)[0])
-
- ix1 = index_of(x, 75)
- ix2 = index_of(x, 135)
- ix3 = index_of(x, 175)
-
- exp_mod.guess(y[:ix1], x=x[:ix1])
- gauss1.guess(y[ix1:ix2], x=x[ix1:ix2])
- gauss2.guess(y[ix2:ix3], x=x[ix2:ix3])
-
-we can get a better initial estimate, and the fit converges in fewer steps,
-getting to identical values (to the precision printed out in the report),
-and without any bounds on parameters at all::
-
- [[Model]]
- Composite Model:
- gaussian(prefix='g1_')
- gaussian(prefix='g2_')
- exponential(prefix='exp_')
- [[Fit Statistics]]
- # function evals = 46
- # data points = 250
- # variables = 8
- chi-square = 1247.528
- reduced chi-square = 5.155
- [[Variables]]
- exp_amplitude: 99.0183281 +/- 0.537487 (0.54%) (init= 94.53724)
- exp_decay: 90.9508863 +/- 1.103105 (1.21%) (init= 111.1985)
- g1_amplitude: 4257.77321 +/- 42.38338 (1.00%) (init= 2126.432)
- g1_center: 107.030954 +/- 0.150067 (0.14%) (init= 106.5)
- g1_fwhm: 39.2609141 +/- 0.377905 (0.96%) == '2.3548200*g1_sigma'
- g1_sigma: 16.6725754 +/- 0.160481 (0.96%) (init= 14.5)
- g2_amplitude: 2493.41766 +/- 36.16948 (1.45%) (init= 1878.892)
- g2_center: 153.270100 +/- 0.194667 (0.13%) (init= 150)
- g2_fwhm: 32.5128777 +/- 0.439866 (1.35%) == '2.3548200*g2_sigma'
- g2_sigma: 13.8069481 +/- 0.186794 (1.35%) (init= 15)
- [[Correlations]] (unreported correlations are < 0.500)
- C(g1_amplitude, g1_sigma) = 0.824
- C(g2_amplitude, g2_sigma) = 0.815
- C(g1_sigma, g2_center) = 0.684
- C(g1_amplitude, g2_center) = 0.648
- C(g1_center, g2_center) = 0.621
- C(g1_center, g1_sigma) = 0.507
-
-
-
-This example is in the file ``doc_nistgauss2.py`` in the examples folder,
-and the fit result shown on the right above shows an improved initial
-estimate of the data.
+.. _builtin_models_chapter:
+
+=====================================================
+Built-in Fitting Models in the :mod:`models` module
+=====================================================
+
+.. module:: models
+
+Lmfit provides several builtin fitting models in the :mod:`models` module.
+These pre-defined models each subclass from the :class:`model.Model` class of the
+previous chapter and wrap relatively well-known functional forms, such as
+Gaussians, Lorentzian, and Exponentials that are used in a wide range of
+scientific domains. In fact, all the models are all based on simple, plain
+python functions defined in the :mod:`lineshapes` module. In addition to
+wrapping a function into a :class:`model.Model`, these models also provide a
+:meth:`guess` method that is intended to give a reasonable
+set of starting values from a data array that closely approximates the
+data to be fit.
+
+As shown in the previous chapter, a key feature of the :class:`mode.Model` class
+is that models can easily be combined to give a composite
+:class:`model.Model`. Thus while some of the models listed here may seem pretty
+trivial (notably, :class:`ConstantModel` and :class:`LinearModel`), the
+main point of having these is to be able to used in composite models. For
+example, a Lorentzian plus a linear background might be represented as::
+
+ >>> from lmfit.models import LinearModel, LorentzianModel
+ >>> peak = LorentzianModel()
+ >>> background = LinearModel()
+ >>> model = peak + background
+
+All the models listed below are one dimensional, with an independent
+variable named ``x``. Many of these models represent a function with a
+distinct peak, and so share common features. To maintain uniformity,
+common parameter names are used whenever possible. Thus, most models have
+a parameter called ``amplitude`` that represents the overall height (or
+area of) a peak or function, a ``center`` parameter that represents a peak
+centroid position, and a ``sigma`` parameter that gives a characteristic
+width. Many peak shapes also have a parameter ``fwhm`` (constrained by
+``sigma``) giving the full width at half maximum and a parameter ``height``
+(constrained by ``sigma`` and ``amplitude``) to give the maximum peak
+height.
+
+After a list of builtin models, a few examples of their use is given.
+
+Peak-like models
+-------------------
+
+There are many peak-like models available. These include
+:class:`GaussianModel`, :class:`LorentzianModel`, :class:`VoigtModel` and
+some less commonly used variations. The :meth:`guess`
+methods for all of these make a fairly crude guess for the value of
+``amplitude``, but also set a lower bound of 0 on the value of ``sigma``.
+
+:class:`GaussianModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: GaussianModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+A model based on a `Gaussian or normal distribution lineshape
+<http://en.wikipedia.org/wiki/Normal_distribution>`_. Parameter names:
+``amplitude``, ``center``, and ``sigma``.
+In addition, parameters ``fwhm`` and ``height`` are included as constraints
+to report full width at half maximum and maximum peak height, respectively.
+
+.. math::
+
+ f(x; A, \mu, \sigma) = \frac{A}{\sigma\sqrt{2\pi}} e^{[{-{(x-\mu)^2}/{{2\sigma}^2}}]}
+
+where the parameter ``amplitude`` corresponds to :math:`A`, ``center`` to
+:math:`\mu`, and ``sigma`` to :math:`\sigma`. The full width at
+half maximum is :math:`2\sigma\sqrt{2\ln{2}}`, approximately
+:math:`2.3548\sigma`
+
+
+:class:`LorentzianModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: LorentzianModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+A model based on a `Lorentzian or Cauchy-Lorentz distribution function
+<http://en.wikipedia.org/wiki/Cauchy_distribution>`_. Parameter names:
+``amplitude``, ``center``, and ``sigma``.
+In addition, parameters ``fwhm`` and ``height`` are included as constraints
+to report full width at half maximum and maximum peak height, respectively.
+
+.. math::
+
+ f(x; A, \mu, \sigma) = \frac{A}{\pi} \big[\frac{\sigma}{(x - \mu)^2 + \sigma^2}\big]
+
+where the parameter ``amplitude`` corresponds to :math:`A`, ``center`` to
+:math:`\mu`, and ``sigma`` to :math:`\sigma`. The full width at
+half maximum is :math:`2\sigma`.
+
+
+:class:`VoigtModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: VoigtModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+A model based on a `Voigt distribution function
+<http://en.wikipedia.org/wiki/Voigt_profile>`_. Parameter names:
+``amplitude``, ``center``, and ``sigma``. A ``gamma`` parameter is also
+available. By default, it is constrained to have value equal to ``sigma``,
+though this can be varied independently. In addition, parameters ``fwhm``
+and ``height`` are included as constraints to report full width at half
+maximum and maximum peak height, respectively. The definition for the
+Voigt function used here is
+
+.. math::
+
+ f(x; A, \mu, \sigma, \gamma) = \frac{A \textrm{Re}[w(z)]}{\sigma\sqrt{2 \pi}}
+
+where
+
+.. math::
+ :nowrap:
+
+ \begin{eqnarray*}
+ z &=& \frac{x-\mu +i\gamma}{\sigma\sqrt{2}} \\
+ w(z) &=& e^{-z^2}{\operatorname{erfc}}(-iz)
+ \end{eqnarray*}
+
+and :func:`erfc` is the complimentary error function. As above,
+``amplitude`` corresponds to :math:`A`, ``center`` to
+:math:`\mu`, and ``sigma`` to :math:`\sigma`. The parameter ``gamma``
+corresponds to :math:`\gamma`.
+If ``gamma`` is kept at the default value (constrained to ``sigma``),
+the full width at half maximum is approximately :math:`3.6013\sigma`.
+
+
+:class:`PseudoVoigtModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: PseudoVoigtModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+a model based on a `pseudo-Voigt distribution function
+<http://en.wikipedia.org/wiki/Voigt_profile#Pseudo-Voigt_Approximation>`_,
+which is a weighted sum of a Gaussian and Lorentzian distribution functions
+with that share values for ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`)
+and full width at half maximum (and so have constrained values of
+``sigma`` (:math:`\sigma`). A parameter ``fraction`` (:math:`\alpha`)
+controls the relative weight of the Gaussian and Lorentzian components,
+giving the full definition of
+
+.. math::
+
+ f(x; A, \mu, \sigma, \alpha) = \frac{(1-\alpha)A}{\sigma_g\sqrt{2\pi}} e^{[{-{(x-\mu)^2}/{{2\sigma_g}^2}}]}
+ + \frac{\alpha A}{\pi} \big[\frac{\sigma}{(x - \mu)^2 + \sigma^2}\big]
+
+where :math:`\sigma_g = {\sigma}/{\sqrt{2\ln{2}}}` so that the full width
+at half maximum of each component and of the sum is :math:`2\sigma`. The
+:meth:`guess` function always sets the starting value for ``fraction`` at 0.5.
+
+
+:class:`MoffatModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: MoffatModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+a model based on a `Moffat distribution function
+<https://en.wikipedia.org/wiki/Moffat_distribution>`_, the parameters are
+``amplitude`` (:math:`A`), ``center`` (:math:`\mu`),
+a width parameter ``sigma`` (:math:`\sigma`) and an exponent ``beta`` (:math:`\beta`).
+For (:math:`\beta=1`) the Moffat has a Lorentzian shape.
+
+.. math::
+
+ f(x; A, \mu, \sigma, \beta) = A \big[(\frac{x-\mu}{\sigma})^2+1\big]^{-\beta}
+
+the full width have maximum is :math:`2\sigma\sqrt{2^{1/\beta}-1}`.
+:meth:`guess` function always sets the starting value for ``beta`` to 1.
+
+
+:class:`Pearson7Model`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: Pearson7Model(missing=None[, prefix=''[, name=None[, **kws]]])
+
+A model based on a `Pearson VII distribution
+<http://en.wikipedia.org/wiki/Pearson_distribution#The_Pearson_type_VII_distribution>`_.
+This is a Lorenztian-like distribution function. It has the usual
+parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
+``sigma`` (:math:`\sigma`), and also an ``exponent`` (:math:`m`) in
+
+.. math::
+
+ f(x; A, \mu, \sigma, m) = \frac{A}{\sigma{\beta(m-\frac{1}{2}, \frac{1}{2})}} \bigl[1 + \frac{(x-\mu)^2}{\sigma^2} \bigr]^{-m}
+
+where :math:`\beta` is the beta function (see :scipydoc:`special.beta` in
+:mod:`scipy.special`). The :meth:`guess` function always
+gives a starting value for ``exponent`` of 1.5.
+
+:class:`StudentsTModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: StudentsTModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+A model based on a `Student's t distribution function
+<http://en.wikipedia.org/wiki/Student%27s_t-distribution>`_, with the usual
+parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
+``sigma`` (:math:`\sigma`) in
+
+.. math::
+
+ f(x; A, \mu, \sigma) = \frac{A \Gamma(\frac{\sigma+1}{2})} {\sqrt{\sigma\pi}\,\Gamma(\frac{\sigma}{2})} \Bigl[1+\frac{(x-\mu)^2}{\sigma}\Bigr]^{-\frac{\sigma+1}{2}}
+
+
+where :math:`\Gamma(x)` is the gamma function.
+
+
+:class:`BreitWignerModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: BreitWignerModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+A model based on a `Breit-Wigner-Fano function
+<http://en.wikipedia.org/wiki/Fano_resonance>`_. It has the usual
+parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
+``sigma`` (:math:`\sigma`), plus ``q`` (:math:`q`) in
+
+.. math::
+
+ f(x; A, \mu, \sigma, q) = \frac{A (q\sigma/2 + x - \mu)^2}{(\sigma/2)^2 + (x - \mu)^2}
+
+
+:class:`LognormalModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: LognormalModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+A model based on the `Log-normal distribution function
+<http://en.wikipedia.org/wiki/Lognormal>`_.
+It has the usual parameters
+``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and ``sigma``
+(:math:`\sigma`) in
+
+.. math::
+
+ f(x; A, \mu, \sigma) = \frac{A e^{-(\ln(x) - \mu)/ 2\sigma^2}}{x}
+
+
+:class:`DampedOcsillatorModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: DampedOcsillatorModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+A model based on the `Damped Harmonic Oscillator Amplitude
+<http://en.wikipedia.org/wiki/Harmonic_oscillator#Amplitude_part>`_.
+It has the usual parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
+``sigma`` (:math:`\sigma`) in
+
+.. math::
+
+ f(x; A, \mu, \sigma) = \frac{A}{\sqrt{ [1 - (x/\mu)^2]^2 + (2\sigma x/\mu)^2}}
+
+
+:class:`ExponentialGaussianModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: ExponentialGaussianModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+A model of an `Exponentially modified Gaussian distribution
+<http://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution>`_.
+It has the usual parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
+``sigma`` (:math:`\sigma`), and also ``gamma`` (:math:`\gamma`) in
+
+.. math::
+
+ f(x; A, \mu, \sigma, \gamma) = \frac{A\gamma}{2}
+ \exp\bigl[\gamma({\mu - x + \gamma\sigma^2/2})\bigr]
+ {\operatorname{erfc}}\Bigl(\frac{\mu + \gamma\sigma^2 - x}{\sqrt{2}\sigma}\Bigr)
+
+
+where :func:`erfc` is the complimentary error function.
+
+:class:`SkewedGaussianModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: SkewedGaussianModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+A variation of the above model, this is a `Skewed normal distribution
+<http://en.wikipedia.org/wiki/Skew_normal_distribution>`_.
+It has the usual parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
+``sigma`` (:math:`\sigma`), and also ``gamma`` (:math:`\gamma`) in
+
+.. math::
+
+ f(x; A, \mu, \sigma, \gamma) = \frac{A}{\sigma\sqrt{2\pi}}
+ e^{[{-{(x-\mu)^2}/{{2\sigma}^2}}]} \Bigl\{ 1 +
+ {\operatorname{erf}}\bigl[
+ \frac{\gamma(x-\mu)}{\sigma\sqrt{2}}
+ \bigr] \Bigr\}
+
+
+where :func:`erf` is the error function.
+
+
+:class:`DonaichModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: DonaichModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+A model of an `Doniach Sunjic asymmetric lineshape
+<http://www.casaxps.com/help_manual/line_shapes.htm>`_, used in
+photo-emission. With the usual parameters ``amplitude`` (:math:`A`),
+``center`` (:math:`\mu`) and ``sigma`` (:math:`\sigma`), and also ``gamma``
+(:math:`\gamma`) in
+
+.. math::
+
+ f(x; A, \mu, \sigma, \gamma) = A\frac{\cos\bigl[\pi\gamma/2 + (1-\gamma)
+ \arctan{(x - \mu)}/\sigma\bigr]} {\bigr[1 + (x-\mu)/\sigma\bigl]^{(1-\gamma)/2}}
+
+
+Linear and Polynomial Models
+------------------------------------
+
+These models correspond to polynomials of some degree. Of course, lmfit is
+a very inefficient way to do linear regression (see :numpydoc:`polyfit`
+or :scipydoc:`stats.linregress`), but these models may be useful as one
+of many components of composite model.
+
+:class:`ConstantModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: ConstantModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+ a class that consists of a single value, ``c``. This is constant in the
+ sense of having no dependence on the independent variable ``x``, not in
+ the sense of being non-varying. To be clear, ``c`` will be a variable
+ Parameter.
+
+:class:`LinearModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: LinearModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+ a class that gives a linear model:
+
+.. math::
+
+ f(x; m, b) = m x + b
+
+with parameters ``slope`` for :math:`m` and ``intercept`` for :math:`b`.
+
+
+:class:`QuadraticModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: QuadraticModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+
+ a class that gives a quadratic model:
+
+.. math::
+
+ f(x; a, b, c) = a x^2 + b x + c
+
+with parameters ``a``, ``b``, and ``c``.
+
+
+:class:`ParabolicModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: ParabolicModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+ same as :class:`QuadraticModel`.
+
+
+:class:`PolynomialModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+
+.. class:: PolynomialModel(degree, missing=None[, prefix=''[, name=None[, **kws]]])
+
+ a class that gives a polynomial model up to ``degree`` (with maximum
+ value of 7).
+
+.. math::
+
+ f(x; c_0, c_1, \ldots, c_7) = \sum_{i=0, 7} c_i x^i
+
+with parameters ``c0``, ``c1``, ..., ``c7``. The supplied ``degree``
+will specify how many of these are actual variable parameters. This uses
+:numpydoc:`polyval` for its calculation of the polynomial.
+
+
+
+Step-like models
+-----------------------------------------------
+
+Two models represent step-like functions, and share many characteristics.
+
+:class:`StepModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: StepModel(form='linear'[, missing=None[, prefix=''[, name=None[, **kws]]]])
+
+A model based on a Step function, with four choices for functional form.
+The step function starts with a value 0, and ends with a value of :math:`A`
+(``amplitude``), rising to :math:`A/2` at :math:`\mu` (``center``),
+with :math:`\sigma` (``sigma``) setting the characteristic width. The
+supported functional forms are ``linear`` (the default), ``atan`` or
+``arctan`` for an arc-tangent function, ``erf`` for an error function, or
+``logistic`` for a `logistic function <http://en.wikipedia.org/wiki/Logistic_function>`_.
+The forms are
+
+.. math::
+ :nowrap:
+
+ \begin{eqnarray*}
+ & f(x; A, \mu, \sigma, {\mathrm{form={}'linear{}'}}) & = A \min{[1, \max{(0, \alpha)}]} \\
+ & f(x; A, \mu, \sigma, {\mathrm{form={}'arctan{}'}}) & = A [1/2 + \arctan{(\alpha)}/{\pi}] \\
+ & f(x; A, \mu, \sigma, {\mathrm{form={}'erf{}'}}) & = A [1 + {\operatorname{erf}}(\alpha)]/2 \\
+ & f(x; A, \mu, \sigma, {\mathrm{form={}'logistic{}'}})& = A [1 - \frac{1}{1 + e^{\alpha}} ]
+ \end{eqnarray*}
+
+where :math:`\alpha = (x - \mu)/{\sigma}`.
+
+:class:`RectangleModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+
+.. class:: RectangleModel(form='linear'[, missing=None[, prefix=''[, name=None[, **kws]]]])
+
+A model based on a Step-up and Step-down function of the same form. The
+same choices for functional form as for :class:`StepModel` are supported,
+with ``linear`` as the default. The function starts with a value 0, and
+ends with a value of :math:`A` (``amplitude``), rising to :math:`A/2` at
+:math:`\mu_1` (``center1``), with :math:`\sigma_1` (``sigma1``) setting the
+characteristic width. It drops to rising to :math:`A/2` at :math:`\mu_2`
+(``center2``), with characteristic width :math:`\sigma_2` (``sigma2``).
+
+.. math::
+ :nowrap:
+
+ \begin{eqnarray*}
+ &f(x; A, \mu, \sigma, {\mathrm{form={}'linear{}'}}) &= A \{ \min{[1, \max{(0, \alpha_1)}]} + \min{[-1, \max{(0, \alpha_2)}]} \} \\
+ &f(x; A, \mu, \sigma, {\mathrm{form={}'arctan{}'}}) &= A [\arctan{(\alpha_1)} + \arctan{(\alpha_2)}]/{\pi} \\
+ &f(x; A, \mu, \sigma, {\mathrm{form={}'erf{}'}}) &= A [{\operatorname{erf}}(\alpha_1) + {\operatorname{erf}}(\alpha_2)]/2 \\
+ &f(x; A, \mu, \sigma, {\mathrm{form={}'logistic{}'}}) &= A [1 - \frac{1}{1 + e^{\alpha_1}} - \frac{1}{1 + e^{\alpha_2}} ]
+ \end{eqnarray*}
+
+
+where :math:`\alpha_1 = (x - \mu_1)/{\sigma_1}` and :math:`\alpha_2 = -(x - \mu_2)/{\sigma_2}`.
+
+
+Exponential and Power law models
+-----------------------------------------------
+
+:class:`ExponentialModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: ExponentialModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+A model based on an `exponential decay function
+<http://en.wikipedia.org/wiki/Exponential_decay>`_. With parameters named
+``amplitude`` (:math:`A`), and ``decay`` (:math:`\tau`), this has the form:
+
+.. math::
+
+ f(x; A, \tau) = A e^{-x/\tau}
+
+
+:class:`PowerLawModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: PowerLawModel(missing=None[, prefix=''[, name=None[, **kws]]])
+
+A model based on a `Power Law <http://en.wikipedia.org/wiki/Power_law>`_.
+With parameters
+named ``amplitude`` (:math:`A`), and ``exponent`` (:math:`k`), this has the
+form:
+
+.. math::
+
+ f(x; A, k) = A x^k
+
+
+User-defined Models
+----------------------------
+
+.. _asteval: http://newville.github.io/asteval/
+
+As shown in the previous chapter (:ref:`model_chapter`), it is fairly
+straightforward to build fitting models from parametrized python functions.
+The number of model classes listed so far in the present chapter should
+make it clear that this process is not too difficult. Still, it is
+sometimes desirable to build models from a user-supplied function. This
+may be especially true if model-building is built-in to some larger library
+or application for fitting in which the user may not be able to easily
+build and use a new model from python code.
+
+
+The :class:`ExpressionModel` allows a model to be built from a
+user-supplied expression. This uses the `asteval`_ module also used for
+mathematical constraints as discussed in :ref:`constraints_chapter`.
+
+
+:class:`ExpressionModel`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. class:: ExpressionModel(expr, independent_vars=None, init_script=None, **kws)
+
+ A model using the user-supplied mathematical expression, which can be nearly any valid Python expresion.
+
+ :param expr: expression use to build model
+ :type expr: string
+ :param independent_vars: list of argument names in expression that are independent variables.
+ :type independent_vars: ``None`` (default) or list of strings for independent variables.
+ :param init_script: python script to run before parsing and evaluating expression.
+ :type init_script: ``None`` (default) or string
+
+with other parameters passed to :class:`model.Model`, with the notable
+exception that :class:`ExpressionModel` does **not** support the `prefix` argument.
+
+Since the point of this model is that an arbitrary expression will be
+supplied, the determination of what are the parameter names for the model
+happens when the model is created. To do this, the expression is parsed,
+and all symbol names are found. Names that are already known (there are
+over 500 function and value names in the asteval namespace, including most
+python builtins, more than 200 functions inherited from numpy, and more
+than 20 common lineshapes defined in the :mod:`lineshapes` module) are not
+converted to parameters. Unrecognized name are expected to be names either
+of parameters or independent variables. If `independent_vars` is the
+default value of ``None``, and if the expression contains a variable named
+`x`, that will be used as the independent variable. Otherwise,
+`independent_vars` must be given.
+
+For example, if one creates an :class:`ExpressionModel` as::
+
+ >>> mod = ExpressionModel('off + amp * exp(-x/x0) * sin(x*phase)')
+
+The name `exp` will be recognized as the exponent function, so the model
+will be interpreted to have parameters named `off`, `amp`, `x0` and
+`phase`. In addition, `x` will be assumed to be the sole independent variable.
+In general, there is no obvious way to set default parameter values or
+parameter hints for bounds, so this will have to be handled explicitly.
+
+To evaluate this model, you might do the following::
+
+ >>> x = numpy.linspace(0, 10, 501)
+ >>> params = mod.make_params(off=0.25, amp=1.0, x0=2.0, phase=0.04)
+ >>> y = mod.eval(params, x=x)
+
+
+While many custom models can be built with a single line expression
+(especially since the names of the lineshapes like `gaussian`, `lorentzian`
+and so on, as well as many numpy functions, are available), more complex
+models will inevitably require multiple line functions. You can include
+such Python code with the `init_script` argument. The text of this script
+is evaluated when the model is initialized (and before the actual
+expression is parsed), so that you can define functions to be used
+in your expression.
+
+As a probably unphysical example, to make a model that is the derivative of
+a Gaussian function times the logarithm of a Lorentzian function you may
+could to define this in a script::
+
+ >>> script = """
+ def mycurve(x, amp, cen, sig):
+ loren = lorentzian(x, amplitude=amp, center=cen, sigma=sig)
+ gauss = gaussian(x, amplitude=amp, center=cen, sigma=sig)
+ return log(loren)*gradient(gauss)/gradient(x)
+ """
+
+and then use this with :class:`ExpressionModel` as::
+
+ >>> mod = ExpressionModel('mycurve(x, height, mid, wid)',
+ init_script=script,
+ independent_vars=['x'])
+
+As above, this will interpret the parameter names to be `height`, `mid`,
+and `wid`, and build a model that can be used to fit data.
+
+
+
+Example 1: Fit Peaked data to Gaussian, Lorentzian, and Voigt profiles
+------------------------------------------------------------------------
+
+Here, we will fit data to three similar line shapes, in order to decide which
+might be the better model. We will start with a Gaussian profile, as in
+the previous chapter, but use the built-in :class:`GaussianModel` instead
+of writing one ourselves. This is a slightly different version rom the
+one in previous example in that the parameter names are different, and have
+built-in default values. We'll simply use::
+
+ from numpy import loadtxt
+ from lmfit.models import GaussianModel
+
+ data = loadtxt('test_peak.dat')
+ x = data[:, 0]
+ y = data[:, 1]
+
+ mod = GaussianModel()
+
+ pars = mod.guess(y, x=x)
+ out = mod.fit(y, pars, x=x)
+ print(out.fit_report(min_correl=0.25))
+
+
+which prints out the results::
+
+ [[Model]]
+ gaussian
+ [[Fit Statistics]]
+ # function evals = 23
+ # data points = 401
+ # variables = 3
+ chi-square = 29.994
+ reduced chi-square = 0.075
+ Akaike info crit = -1030.763
+ Bayesian info crit = -1018.781
+ [[Variables]]
+ sigma: 1.23218319 +/- 0.007374 (0.60%) (init= 1.35)
+ fwhm: 2.90156963 +/- 0.017366 (0.60%) == '2.3548200*sigma'
+ height: 9.81457973 +/- 0.050872 (0.52%) == '0.3989423*amplitude/sigma'
+ center: 9.24277049 +/- 0.007374 (0.08%) (init= 9.25)
+ amplitude: 30.3135571 +/- 0.157126 (0.52%) (init= 29.08159)
+ [[Correlations]] (unreported correlations are < 0.250)
+ C(sigma, amplitude) = 0.577
+
+We see a few interesting differences from the results of the previous
+chapter. First, the parameter names are longer. Second, there are ``fwhm``
+and ``height`` parameters, to give the full width at half maximum and
+maximum peak height. And third, the automated initial guesses are pretty
+good. A plot of the fit:
+
+.. _figA1:
+
+ .. image:: _images/models_peak1.png
+ :target: _images/models_peak1.png
+ :width: 48 %
+ .. image:: _images/models_peak2.png
+ :target: _images/models_peak2.png
+ :width: 48 %
+
+ Fit to peak with Gaussian (left) and Lorentzian (right) models.
+
+shows a decent match to the data -- the fit worked with no explicit setting
+of initial parameter values. Looking more closing, the fit is not perfect,
+especially in the tails of the peak, suggesting that a different peak
+shape, with longer tails, should be used. Perhaps a Lorentzian would be
+better? To do this, we simply replace ``GaussianModel`` with
+``LorentzianModel`` to get a :class:`LorentzianModel`::
+
+ from lmfit.models import LorentzianModel
+ mod = LorentzianModel()
+
+with the rest of the script as above. Perhaps predictably, the first thing
+we try gives results that are worse::
+
+ [[Model]]
+ Model(lorentzian)
+ [[Fit Statistics]]
+ # function evals = 27
+ # data points = 401
+ # variables = 3
+ chi-square = 53.754
+ reduced chi-square = 0.135
+ Akaike info crit = -796.819
+ Bayesian info crit = -784.837
+ [[Variables]]
+ sigma: 1.15484517 +/- 0.013156 (1.14%) (init= 1.35)
+ fwhm: 2.30969034 +/- 0.026312 (1.14%) == '2.0000000*sigma'
+ height: 10.7420881 +/- 0.086336 (0.80%) ==
+ '0.3183099*amplitude/sigm a'
+ center: 9.24438944 +/- 0.009275 (0.10%) (init= 9.25)
+ amplitude: 38.9728645 +/- 0.313857 (0.81%) (init= 36.35199)
+ [[Correlations]] (unreported correlations are < 0.250)
+ C(sigma, amplitude) = 0.709
+
+
+with the plot shown on the right in the figure above. The tails are now
+too big, and the value for :math:`\chi^2` almost doubled. A Voigt model
+does a better job. Using :class:`VoigtModel`, this is as simple as using::
+
+ from lmfit.models import VoigtModel
+ mod = VoigtModel()
+
+with all the rest of the script as above. This gives::
+
+ [[Model]]
+ Model(voigt)
+ [[Fit Statistics]]
+ # function evals = 19
+ # data points = 401
+ # variables = 3
+ chi-square = 14.545
+ reduced chi-square = 0.037
+ Akaike info crit = -1320.995
+ Bayesian info crit = -1309.013
+ [[Variables]]
+ sigma: 0.73015574 +/- 0.003684 (0.50%) (init= 0.8775)
+ gamma: 0.73015574 +/- 0.003684 (0.50%) == 'sigma'
+ fwhm: 2.62951718 +/- 0.013269 (0.50%) == '3.6013100*sigma'
+ height: 19.5360268 +/- 0.075691 (0.39%) == '0.3989423*amplitude/sigm a'
+ center: 9.24411142 +/- 0.005054 (0.05%) (init= 9.25)
+ amplitude: 35.7554017 +/- 0.138614 (0.39%) (init= 43.62238)
+ [[Correlations]] (unreported correlations are < 0.250)
+ C(sigma, amplitude) = 0.651
+
+
+which has a much better value for :math:`\chi^2` and an obviously better
+match to the data as seen in the figure below (left).
+
+.. _figA2:
+
+ .. image:: _images/models_peak3.png
+ :target: _images/models_peak3.png
+ :width: 48 %
+ .. image:: _images/models_peak4.png
+ :target: _images/models_peak4.png
+ :width: 48 %
+
+ Fit to peak with Voigt model (left) and Voigt model with ``gamma``
+ varying independently of ``sigma`` (right).
+
+Can we do better? The Voigt function has a :math:`\gamma` parameter
+(``gamma``) that can be distinct from ``sigma``. The default behavior used
+above constrains ``gamma`` to have exactly the same value as ``sigma``. If
+we allow these to vary separately, does the fit improve? To do this, we
+have to change the ``gamma`` parameter from a constrained expression and
+give it a starting value using something like::
+
+ mod = VoigtModel()
+ pars = mod.guess(y, x=x)
+ pars['gamma'].set(value=0.7, vary=True, expr='')
+
+
+which gives::
+
+ [[Model]]
+ Model(voigt)
+ [[Fit Statistics]]
+ # function evals = 23
+ # data points = 401
+ # variables = 4
+ chi-square = 10.930
+ reduced chi-square = 0.028
+ Akaike info crit = -1432.556
+ Bayesian info crit = -1416.580
+ [[Variables]]
+ sigma: 0.89518950 +/- 0.014154 (1.58%) (init= 0.8775)
+ gamma: 0.52540156 +/- 0.018579 (3.54%) (init= 0.7)
+ fwhm: 3.22385492 +/- 0.050974 (1.58%) == '3.6013100*sigma'
+ height: 15.2374711 +/- 0.299235 (1.96%) ==
+ '0.3989423*amplitude/sigm a'
+ center: 9.24374845 +/- 0.004419 (0.05%) (init= 9.25)
+ amplitude: 34.1914716 +/- 0.179468 (0.52%) (init= 43.62238)
+ [[Correlations]] (unreported correlations are < 0.250)
+ C(sigma, gamma) = -0.928
+ C(gamma, amplitude) = 0.821
+ C(sigma, amplitude) = -0.651
+
+and the fit shown on the right above.
+
+Comparing the two fits with the Voigt function, we see that :math:`\chi^2`
+is definitely improved with a separately varying ``gamma`` parameter. In
+addition, the two values for ``gamma`` and ``sigma`` differ significantly
+-- well outside the estimated uncertainties. More compelling, reduced
+:math:`\chi^2` is improved even though a fourth variable has been added to
+the fit. In the simplest statistical sense, this suggests that ``gamma``
+is a significant variable in the model. In addition, we can use both the
+Akaike or Bayesian Information Criteria (see
+:ref:`information_criteria_label`) to assess how likely the model with
+variable ``gamma`` is to explain the data than the model with ``gamma``
+fixed to the value of ``sigma``. According to theory,
+:math:`\exp(-(\rm{AIC1}-\rm{AIC0})/2)` gives the probably that a model with
+AIC` is more likely than a model with AIC0. For the two models here, with
+AIC values of -1432 and -1321 (Note: if we had more carefully set the value
+for ``weights`` based on the noise in the data, these values might be
+positive, but there difference would be roughly the same), this says that
+the model with ``gamma`` fixed to ``sigma`` has a probably less than 1.e-25
+of being the better model.
+
+
+Example 2: Fit data to a Composite Model with pre-defined models
+------------------------------------------------------------------
+
+Here, we repeat the point made at the end of the last chapter that
+instances of :class:`model.Model` class can be added together to make a
+*composite model*. By using the large number of built-in models available,
+it is therefore very simple to build models that contain multiple peaks and
+various backgrounds. An example of a simple fit to a noisy step function
+plus a constant:
+
+.. literalinclude:: ../examples/doc_stepmodel.py
+
+After constructing step-like data, we first create a :class:`StepModel`
+telling it to use the ``erf`` form (see details above), and a
+:class:`ConstantModel`. We set initial values, in one case using the data
+and :meth:`guess` method for the initial step function paramaters, and
+:meth:`make_params` arguments for the linear component.
+After making a composite model, we run :meth:`fit` and report the
+results, which gives::
+
+ [[Model]]
+ [[Model]]
+ (Model(step, prefix='step_', form='erf') + Model(linear, prefix='line_'))
+ [[Fit Statistics]]
+ # function evals = 51
+ # data points = 201
+ # variables = 5
+ chi-square = 648.584
+ reduced chi-square = 3.309
+ Akaike info crit = 250.532
+ Bayesian info crit = 267.048
+ [[Variables]]
+ line_slope: 2.06986083 +/- 0.097005 (4.69%) (init= 0)
+ line_intercept: 11.7526825 +/- 0.288725 (2.46%) (init= 10.7017)
+ step_center: 3.12329688 +/- 0.005441 (0.17%) (init= 2.5)
+ step_sigma: 0.67050317 +/- 0.011480 (1.71%) (init= 1.428571)
+ step_amplitude: 111.673928 +/- 0.681024 (0.61%) (init= 134.6809)
+ [[Correlations]] (unreported correlations are < 0.100)
+ C(line_slope, step_amplitude) = -0.878
+ C(step_sigma, step_amplitude) = 0.563
+ C(line_slope, step_sigma) = -0.455
+ C(line_intercept, step_center) = 0.426
+ C(line_slope, line_intercept) = -0.307
+ C(line_slope, step_center) = -0.234
+ C(line_intercept, step_sigma) = -0.139
+ C(line_intercept, step_amplitude) = -0.122
+ C(step_center, step_amplitude) = 0.108
+
+with a plot of
+
+.. image:: _images/models_stepfit.png
+ :target: _images/models_stepfit.png
+ :width: 50 %
+
+
+Example 3: Fitting Multiple Peaks -- and using Prefixes
+------------------------------------------------------------------
+
+.. _NIST StRD: http://itl.nist.gov/div898/strd/nls/nls_main.shtml
+
+As shown above, many of the models have similar parameter names. For
+composite models, this could lead to a problem of having parameters for
+different parts of the model having the same name. To overcome this, each
+:class:`model.Model` can have a ``prefix`` attribute (normally set to a blank
+string) that will be put at the beginning of each parameter name. To
+illustrate, we fit one of the classic datasets from the `NIST StRD`_ suite
+involving a decaying exponential and two gaussians.
+
+.. literalinclude:: ../examples/doc_nistgauss.py
+
+where we give a separate prefix to each model (they all have an
+``amplitude`` parameter). The ``prefix`` values are attached transparently
+to the models.
+
+Note that the calls to :meth:`make_param` used the bare name, without the
+prefix. We could have used the prefixes, but because we used the
+individual model ``gauss1`` and ``gauss2``, there was no need.
+
+Note also in the example here that we explicitly set bounds on many of the
+parameter values.
+
+The fit results printed out are::
+
+ [[Model]]
+ ((Model(gaussian, prefix='g1_') + Model(gaussian, prefix='g2_')) + Model(exponential, prefix='exp_'))
+ [[Fit Statistics]]
+ # function evals = 66
+ # data points = 250
+ # variables = 8
+ chi-square = 1247.528
+ reduced chi-square = 5.155
+ Akaike info crit = 425.995
+ Bayesian info crit = 454.167
+ [[Variables]]
+ exp_amplitude: 99.0183282 +/- 0.537487 (0.54%) (init= 162.2102)
+ exp_decay: 90.9508861 +/- 1.103105 (1.21%) (init= 93.24905)
+ g1_amplitude: 4257.77318 +/- 42.38336 (1.00%) (init= 2000)
+ g1_sigma: 16.6725753 +/- 0.160481 (0.96%) (init= 15)
+ g1_center: 107.030954 +/- 0.150067 (0.14%) (init= 105)
+ g1_fwhm: 39.2609137 +/- 0.377905 (0.96%) == '2.3548200*g1_sigma'
+ g1_height: 101.880231 +/- 0.592170 (0.58%) ==
+ '0.3989423*g1_amplitude/g1_ sigma'
+ g2_amplitude: 2493.41770 +/- 36.16947 (1.45%) (init= 2000)
+ g2_sigma: 13.8069484 +/- 0.186794 (1.35%) (init= 15)
+ g2_center: 153.270100 +/- 0.194667 (0.13%) (init= 155)
+ g2_fwhm: 32.5128783 +/- 0.439866 (1.35%) == '2.3548200*g2_sigma'
+ g2_height: 72.0455934 +/- 0.617220 (0.86%) ==
+ '0.3989423*g2_amplitude/g2_ sigma'
+ [[Correlations]] (unreported correlations are < 0.500)
+ C(g1_amplitude, g1_sigma) = 0.824
+ C(g2_amplitude, g2_sigma) = 0.815
+ C(exp_amplitude, exp_decay) = -0.695
+ C(g1_sigma, g2_center) = 0.684
+ C(g1_center, g2_amplitude) = -0.669
+ C(g1_center, g2_sigma) = -0.652
+ C(g1_amplitude, g2_center) = 0.648
+ C(g1_center, g2_center) = 0.621
+ C(g1_sigma, g1_center) = 0.507
+ C(exp_decay, g1_amplitude) = -0.507
+
+
+We get a very good fit to this problem (described at the NIST site as of
+average difficulty, but the tests there are generally deliberately challenging) by
+applying reasonable initial guesses and putting modest but explicit bounds
+on the parameter values. This fit is shown on the left:
+
+.. _figA3:
+
+ .. image:: _images/models_nistgauss.png
+ :target: _images/models_nistgauss.png
+ :width: 48 %
+ .. image:: _images/models_nistgauss2.png
+ :target: _images/models_nistgauss2.png
+ :width: 48 %
+
+
+One final point on setting initial values. From looking at the data
+itself, we can see the two Gaussian peaks are reasonably well separated but
+do overlap. Furthermore, we can tell that the initial guess for the
+decaying exponential component was poorly estimated because we used the
+full data range. We can simplify the initial parameter values by using
+this, and by defining an :func:`index_of` function to limit the data range.
+That is, with::
+
+ def index_of(arrval, value):
+ "return index of array *at or below* value "
+ if value < min(arrval): return 0
+ return max(np.where(arrval<=value)[0])
+
+ ix1 = index_of(x, 75)
+ ix2 = index_of(x, 135)
+ ix3 = index_of(x, 175)
+
+ exp_mod.guess(y[:ix1], x=x[:ix1])
+ gauss1.guess(y[ix1:ix2], x=x[ix1:ix2])
+ gauss2.guess(y[ix2:ix3], x=x[ix2:ix3])
+
+we can get a better initial estimate. The fit converges to the same answer,
+giving to identical values (to the precision printed out in the report),
+but in few steps, and without any bounds on parameters at all::
+
+ [[Model]]
+ ((Model(gaussian, prefix='g1_') + Model(gaussian, prefix='g2_')) + Model(exponential, prefix='exp_'))
+ [[Fit Statistics]]
+ # function evals = 48
+ # data points = 250
+ # variables = 8
+ chi-square = 1247.528
+ reduced chi-square = 5.155
+ Akaike info crit = 425.995
+ Bayesian info crit = 454.167
+ [[Variables]]
+ exp_amplitude: 99.0183281 +/- 0.537487 (0.54%) (init= 94.53724)
+ exp_decay: 90.9508862 +/- 1.103105 (1.21%) (init= 111.1985)
+ g1_amplitude: 4257.77322 +/- 42.38338 (1.00%) (init= 2126.432)
+ g1_sigma: 16.6725754 +/- 0.160481 (0.96%) (init= 14.5)
+ g1_center: 107.030954 +/- 0.150067 (0.14%) (init= 106.5)
+ g1_fwhm: 39.2609141 +/- 0.377905 (0.96%) == '2.3548200*g1_sigma'
+ g1_height: 101.880231 +/- 0.592171 (0.58%) ==
+ '0.3989423*g1_amplitude/g1_ sigma'
+ g2_amplitude: 2493.41766 +/- 36.16947 (1.45%) (init= 1878.892)
+ g2_sigma: 13.8069481 +/- 0.186794 (1.35%) (init= 15)
+ g2_center: 153.270100 +/- 0.194667 (0.13%) (init= 150)
+ g2_fwhm: 32.5128777 +/- 0.439866 (1.35%) == '2.3548200*g2_sigma'
+ g2_height: 72.0455935 +/- 0.617221 (0.86%) ==
+ '0.3989423*g2_amplitude/g2_ sigma'
+ [[Correlations]] (unreported correlations are < 0.500)
+ C(g1_amplitude, g1_sigma) = 0.824
+ C(g2_amplitude, g2_sigma) = 0.815
+ C(exp_amplitude, exp_decay) = -0.695
+ C(g1_sigma, g2_center) = 0.684
+ C(g1_center, g2_amplitude) = -0.669
+ C(g1_center, g2_sigma) = -0.652
+ C(g1_amplitude, g2_center) = 0.648
+ C(g1_center, g2_center) = 0.621
+ C(g1_sigma, g1_center) = 0.507
+ C(exp_decay, g1_amplitude) = -0.507
+
+
+This script is in the file ``doc_nistgauss2.py`` in the examples folder,
+and the fit result shown on the right above shows an improved initial
+estimate of the data.
diff --git a/doc/conf.py b/doc/conf.py
index e452697..490a01d 100644
--- a/doc/conf.py
+++ b/doc/conf.py
@@ -1,176 +1,187 @@
-# -*- coding: utf-8 -*-
-#
-# lmfit documentation build configuration file
-#
-# This file is execfile()d with the current directory set to its containing dir.
-#
-# Note that not all possible configuration values are present in this
-# autogenerated file.
-#
-# All configuration values have a default; values that are commented out
-# serve to show the default.
-
-import sys, os
-
-# If extensions (or modules to document with autodoc) are in another directory,
-# add these directories to sys.path here. If the directory is relative to the
-# documentation root, use os.path.abspath to make it absolute, like shown here.
-sys.path.append(os.path.abspath(os.path.join('..', 'lmfit')))
-sys.path.append(os.path.abspath(os.path.join('.', 'sphinx')))
-sys.path.append(os.path.abspath(os.path.join('.')))
-# -- General configuration -----------------------------------------------------
-
-# Add any Sphinx extension module names here, as strings. They can be extensions
-# coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
-from extensions import extensions
-
-try:
- import IPython.sphinxext.ipython_directive
- extensions.extend(['IPython.sphinxext.ipython_directive',
- 'IPython.sphinxext.ipython_console_highlighting'])
-except ImportError:
- pass
-
-
-intersphinx_mapping = {'py': ('http://docs.python.org/2', None),
- 'numpy': ('http://docs.scipy.org/doc/numpy/', None),
- 'scipy': ('http://docs.scipy.org/doc/scipy/reference/', None),
- }
-
-intersphinx_cache_limit = 10
-
-# Add any paths that contain templates here, relative to this directory.
-templates_path = ['_templates']
-
-# The suffix of source filenames.
-source_suffix = '.rst'
-
-# The encoding of source files.
-#source_encoding = 'utf-8'
-
-# The master toctree document.
-master_doc = 'index'
-
-# General information about the project.
-project = u'lmfit'
-copyright = u'2014, Matthew Newville, The University of Chicago, Till Stensitzki, Freie Universitat Berlin'
-
-# The version info for the project you're documenting, acts as replacement for
-# |version| and |release|, also used in various other places throughout the
-# built documents.
-#
-# The short X.Y version.
-try:
- import lmfit
- release = lmfit.__version__
-# The full version, including alpha/beta/rc tags.
-except ImportError:
- release = 'latest'
-
-# The language for content autogenerated by Sphinx. Refer to documentation
-# for a list of supported languages.
-#language = None
-
-# There are two options for replacing |today|: either, you set today to some
-# non-false value, then it is used:
-#today = ''
-# Else, today_fmt is used as the format for a strftime call.
-#today_fmt = '%B %d, %Y'
-
-# List of documents that shouldn't be included in the build.
-#unused_docs = []
-
-# List of directories, relative to source directory, that shouldn't be searched
-# for source files.
-exclude_trees = ['_build']
-
-# The reST default role (used for this markup: `text`) to use for all documents.
-#default_role = None
-
-# If true, '()' will be appended to :func: etc. cross-reference text.
-add_function_parentheses = True
-
-# If true, the current module name will be prepended to all description
-# unit titles (such as .. function::).
-add_module_names = False
-
-# If true, sectionauthor and moduleauthor directives will be shown in the
-# output. They are ignored by default.
-#show_authors = False
-
-# The name of the Pygments (syntax highlighting) style to use.
-pygments_style = 'sphinx'
-
-# A list of ignored prefixes for module index sorting.
-#modindex_common_prefix = []
-
-
-# -- Options for HTML output ---------------------------------------------------
-
-html_theme_path = ['sphinx/theme']
-html_theme = 'lmfitdoc'
-
-# Add any paths that contain custom themes here, relative to this directory.
-#html_theme_path = []
-
-# The name for this set of Sphinx documents. If None, it defaults to
-# "<project> v<release> documentation".
-#html_title = None
-html_title = 'Non-Linear Least-Squares Minimization and Curve-Fitting for Python'
-
-# A shorter title for the navigation bar. Default is the same as html_title.
-html_short_title = 'Minimization and Curve-Fitting for Python'
-
-# The name of an image file (relative to this directory) to place at the top
-# of the sidebar.
-#html_logo = None
-
-# The name of an image file (within the static path) to use as favicon of the
-# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32
-# pixels large.
-#html_favicon = None
-
-# Add any paths that contain custom static files (such as style sheets) here,
-# relative to this directory. They are copied after the builtin static files,
-# so a file named "default.css" will overwrite the builtin "default.css".
-html_static_path = ['_static']
-
-# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
-# using the given strftime format.
-#html_last_updated_fmt = '%b %d, %Y'
-
-# If true, SmartyPants will be used to convert quotes and dashes to
-# typographically correct entities.
-html_use_smartypants = True
-
-# Custom sidebar templates, maps document names to template names.
-html_sidebars = {'index': ['indexsidebar.html','searchbox.html']}
-
-html_domain_indices = False
-html_use_index = True
-#html_split_index = False
-
-# If true, links to the reST sources are added to the pages.
-html_show_sourcelink = True
-
-# If true, an OpenSearch description file will be output, and all pages will
-# contain a <link> tag referring to it. The value of this option must be the
-# base URL from which the finished HTML is served.
-#html_use_opensearch = ''
-
-# If nonempty, this is the file name suffix for HTML files (e.g. ".xhtml").
-#html_file_suffix = ''
-
-# Output file base name for HTML help builder.
-htmlhelp_basename = 'lmfitdoc'
-
-# -- Options for LaTeX output --------------------------------------------------
-
-# Grouping the document tree into LaTeX files. List of tuples
-# (source start file, target name, title, author, documentclass [howto/manual]).
-latex_documents = [
- ('index', 'lmfit.tex',
- 'Non-Linear Least-Squares Minimization and Curve-Fitting for Python',
- 'Matthew Newville, Till Stensitzki, and others', 'manual'),
-]
-
+# -*- coding: utf-8 -*-
+#
+# lmfit documentation build configuration file
+#
+# This file is execfile()d with the current directory set to its containing dir.
+#
+# Note that not all possible configuration values are present in this
+# autogenerated file.
+#
+# All configuration values have a default; values that are commented out
+# serve to show the default.
+
+import sys, os
+
+# If extensions (or modules to document with autodoc) are in another directory,
+# add these directories to sys.path here. If the directory is relative to the
+# documentation root, use os.path.abspath to make it absolute, like shown here.
+sys.path.append(os.path.abspath(os.path.join('..', 'lmfit')))
+sys.path.append(os.path.abspath(os.path.join('.', 'sphinx')))
+sys.path.append(os.path.abspath(os.path.join('.')))
+# -- General configuration -----------------------------------------------------
+
+# Add any Sphinx extension module names here, as strings. They can be extensions
+# coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
+from extensions import extensions
+
+extensions = [
+ 'sphinx.ext.extlinks',
+ 'sphinx.ext.autodoc',
+ 'sphinx.ext.napoleon',
+ 'sphinx.ext.mathjax',
+ ]
+
+try:
+ import IPython.sphinxext.ipython_directive
+ extensions.extend(['IPython.sphinxext.ipython_directive',
+ 'IPython.sphinxext.ipython_console_highlighting'])
+except ImportError:
+ pass
+
+intersphinx_mapping = {'py': ('http://docs.python.org/2', None),
+ 'numpy': ('http://docs.scipy.org/doc/numpy/', None),
+ 'scipy': ('http://docs.scipy.org/doc/scipy/reference/', None),
+ }
+
+## intersphinx_cache_limit = 10
+
+extlinks = {
+ 'scipydoc' : ('http://docs.scipy.org/doc/scipy/reference/generated/%s.html', ''),
+ 'numpydoc' : ('http://docs.scipy.org/doc/numpy/reference/generated/numpy.%s.html', ''),
+ }
+
+# Add any paths that contain templates here, relative to this directory.
+templates_path = ['_templates']
+
+# The suffix of source filenames.
+source_suffix = '.rst'
+
+# The encoding of source files.
+#source_encoding = 'utf-8'
+
+# The master toctree document.
+master_doc = 'index'
+
+# General information about the project.
+project = u'lmfit'
+copyright = u'2014, Matthew Newville, The University of Chicago, Till Stensitzki, Freie Universitat Berlin'
+
+# The version info for the project you're documenting, acts as replacement for
+# |version| and |release|, also used in various other places throughout the
+# built documents.
+#
+# The short X.Y version.
+sys.path.insert(0, os.path.abspath('../'))
+try:
+ import lmfit
+ release = lmfit.__version__
+# The full version, including alpha/beta/rc tags.
+except ImportError:
+ release = 'latest'
+
+# The language for content autogenerated by Sphinx. Refer to documentation
+# for a list of supported languages.
+#language = None
+
+# There are two options for replacing |today|: either, you set today to some
+# non-false value, then it is used:
+#today = ''
+# Else, today_fmt is used as the format for a strftime call.
+#today_fmt = '%B %d, %Y'
+
+# List of documents that shouldn't be included in the build.
+#unused_docs = []
+
+# List of directories, relative to source directory, that shouldn't be searched
+# for source files.
+exclude_trees = ['_build']
+
+# The reST default role (used for this markup: `text`) to use for all documents.
+#default_role = None
+
+# If true, '()' will be appended to :func: etc. cross-reference text.
+add_function_parentheses = True
+
+# If true, the current module name will be prepended to all description
+# unit titles (such as .. function::).
+add_module_names = False
+
+# If true, sectionauthor and moduleauthor directives will be shown in the
+# output. They are ignored by default.
+#show_authors = False
+
+# The name of the Pygments (syntax highlighting) style to use.
+pygments_style = 'sphinx'
+
+# A list of ignored prefixes for module index sorting.
+#modindex_common_prefix = []
+
+
+# -- Options for HTML output ---------------------------------------------------
+
+html_theme_path = ['sphinx/theme']
+html_theme = 'lmfitdoc'
+
+# Add any paths that contain custom themes here, relative to this directory.
+#html_theme_path = []
+
+# The name for this set of Sphinx documents. If None, it defaults to
+# "<project> v<release> documentation".
+#html_title = None
+html_title = 'Non-Linear Least-Squares Minimization and Curve-Fitting for Python'
+
+# A shorter title for the navigation bar. Default is the same as html_title.
+html_short_title = 'Minimization and Curve-Fitting for Python'
+
+# The name of an image file (relative to this directory) to place at the top
+# of the sidebar.
+#html_logo = None
+
+# The name of an image file (within the static path) to use as favicon of the
+# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32
+# pixels large.
+#html_favicon = None
+
+# Add any paths that contain custom static files (such as style sheets) here,
+# relative to this directory. They are copied after the builtin static files,
+# so a file named "default.css" will overwrite the builtin "default.css".
+html_static_path = ['_static']
+
+# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
+# using the given strftime format.
+#html_last_updated_fmt = '%b %d, %Y'
+
+# If true, SmartyPants will be used to convert quotes and dashes to
+# typographically correct entities.
+html_use_smartypants = True
+
+# Custom sidebar templates, maps document names to template names.
+html_sidebars = {'index': ['indexsidebar.html','searchbox.html']}
+
+html_domain_indices = False
+html_use_index = True
+#html_split_index = False
+
+# If true, links to the reST sources are added to the pages.
+html_show_sourcelink = True
+
+# If true, an OpenSearch description file will be output, and all pages will
+# contain a <link> tag referring to it. The value of this option must be the
+# base URL from which the finished HTML is served.
+#html_use_opensearch = ''
+
+# If nonempty, this is the file name suffix for HTML files (e.g. ".xhtml").
+#html_file_suffix = ''
+
+# Output file base name for HTML help builder.
+htmlhelp_basename = 'lmfitdoc'
+
+# -- Options for LaTeX output --------------------------------------------------
+
+# Grouping the document tree into LaTeX files. List of tuples
+# (source start file, target name, title, author, documentclass [howto/manual]).
+latex_documents = [
+ ('index', 'lmfit.tex',
+ 'Non-Linear Least-Squares Minimization and Curve-Fitting for Python',
+ 'Matthew Newville, Till Stensitzki, and others', 'manual'),
+]
diff --git a/doc/confidence.rst b/doc/confidence.rst
index c678dfb..67c4f97 100644
--- a/doc/confidence.rst
+++ b/doc/confidence.rst
@@ -1,177 +1,193 @@
-.. _confidence_chapter:
-
-Calculation of confidence intervals
-====================================
-
-.. module:: confidence
-
-The lmfit :mod:`confidence` module allows you to explicitly calculate
-confidence intervals for variable parameters. For most models, it is not
-necessary: the estimation of the standard error from the estimated
-covariance matrix is normally quite good.
-
-But for some models, e.g. a sum of two exponentials, the approximation
-begins to fail. For this case, lmfit has the function :func:`conf_interval`
-to calculate confidence intervals directly. This is substantially slower
-than using the errors estimated from the covariance matrix, but the results
-are more robust.
-
-
-Method used for calculating confidence intervals
--------------------------------------------------
-
-The F-test is used to compare our null model, which is the best fit we have
-found, with an alternate model, where one of the parameters is fixed to a
-specific value. The value is changed until the difference between :math:`\chi^2_0`
-and :math:`\chi^2_{f}` can't be explained by the loss of a degree of freedom
-within a certain confidence.
-
-.. math::
-
- F(P_{fix},N-P) = \left(\frac{\chi^2_f}{\chi^2_{0}}-1\right)\frac{N-P}{P_{fix}}
-
-N is the number of data-points, P the number of parameter of the null model.
-:math:`P_{fix}` is the number of fixed parameters (or to be more clear, the
-difference of number of parameters between our null model and the alternate
-model).
-
-Adding a log-likelihood method is under consideration.
-
-A basic example
----------------
-
-First we create an example problem::
-
- >>> import lmfit
- >>> import numpy as np
- >>> x = np.linspace(0.3,10,100)
- >>> y = 1/(0.1*x)+2+0.1*np.random.randn(x.size)
- >>> pars = lmfit.Parameters()
- >>> pars.add_many(('a', 0.1), ('b', 1))
- >>> def residual(p):
- ... a = p['a'].value
- ... b = p['b'].value
- ... return 1/(a*x)+b-y
-
-
-before we can generate the confidence intervals, we have to run a fit, so
-that the automated estimate of the standard errors can be used as a
-starting point::
-
-
- >>> mini = lmfit.Minimizer(residual, pars)
- >>> result = mini.minimize()
- >>> print(lmfit.fit_report(result.params))
- [Variables]]
- a: 0.09943895 +/- 0.000193 (0.19%) (init= 0.1)
- b: 1.98476945 +/- 0.012226 (0.62%) (init= 1)
- [[Correlations]] (unreported correlations are < 0.100)
- C(a, b) = 0.601
-
-Now it is just a simple function call to calculate the confidence
-intervals::
-
- >>> ci = lmfit.conf_interval(mini, result)
- >>> lmfit.printfuncs.report_ci(ci)
- 99.70% 95.00% 67.40% 0.00% 67.40% 95.00% 99.70%
- a 0.09886 0.09905 0.09925 0.09944 0.09963 0.09982 0.10003
- b 1.94751 1.96049 1.97274 1.97741 1.99680 2.00905 2.02203
-
-This shows the best-fit values for the parameters in the `0.00%` column,
-and parameter values that are at the varying confidence levels given by
-steps in :math:`\sigma`. As we can see, the estimated error is almost the
-same, and the uncertainties are well behaved: Going from 1 :math:`\sigma`
-(68% confidence) to 3 :math:`\sigma` (99.7% confidence) uncertainties is
-fairly linear. It can also be seen that the errors are fairy symmetric
-around the best fit value. For this problem, it is not necessary to
-calculate confidence intervals, and the estimates of the uncertainties from
-the covariance matrix are sufficient.
-
-An advanced example
--------------------
-
-Now we look at a problem where calculating the error from approximated
-covariance can lead to misleading result -- two decaying exponentials. In
-fact such a problem is particularly hard for the Levenberg-Marquardt
-method, so we fitst estimate the results using the slower but robust
-Nelder-Mead method, and *then* use Levenberg-Marquardt to estimate the
-uncertainties and correlations
-
-
-.. literalinclude:: ../examples/doc_confidence2.py
-
-which will report::
-
- [[Variables]]
- a1: 2.98622120 +/- 0.148671 (4.98%) (init= 2.986237)
- a2: -4.33526327 +/- 0.115275 (2.66%) (init=-4.335256)
- t1: 1.30994233 +/- 0.131211 (10.02%) (init= 1.309932)
- t2: 11.8240350 +/- 0.463164 (3.92%) (init= 11.82408)
- [[Correlations]] (unreported correlations are < 0.500)
- C(a2, t2) = 0.987
- C(a2, t1) = -0.925
- C(t1, t2) = -0.881
- C(a1, t1) = -0.599
- 95.00% 68.00% 0.00% 68.00% 95.00%
- a1 2.71850 2.84525 2.98622 3.14874 3.34076
- a2 -4.63180 -4.46663 -4.33526 -4.22883 -4.14178
- t2 10.82699 11.33865 11.82404 12.28195 12.71094
- t1 1.08014 1.18566 1.30994 1.45566 1.62579
-
-
-Again we called :func:`conf_interval`, this time with tracing and only for
-1- and 2 :math:`\sigma`. Comparing these two different estimates, we see
-that the estimate for `a1` is reasonably well approximated from the
-covariance matrix, but the estimates for `a2` and especially for `t1`, and
-`t2` are very asymmetric and that going from 1 :math:`\sigma` (68%
-confidence) to 2 :math:`\sigma` (95% confidence) is not very predictable.
-
-Let plots mad of the confidence region are shown the figure on the left
-below for ``a1`` and ``t2``, and for ``a2`` and ``t2`` on the right:
-
-.. _figC1:
-
- .. image:: _images/conf_interval1.png
- :target: _images/conf_interval1.png
- :width: 48%
- .. image:: _images/conf_interval1a.png
- :target: _images/conf_interval1a.png
- :width: 48%
-
-Neither of these plots is very much like an ellipse, which is implicitly
-assumed by the approach using the covariance matrix.
-
-The trace returned as the optional second argument from
-:func:`conf_interval` contains a dictionary for each variable parameter.
-The values are dictionaries with arrays of values for each variable, and an
-array of corresponding probabilities for the corresponding cumulative
-variables. This can be used to show the dependence between two
-parameters::
-
- >>> x, y, prob = trace['a1']['a1'], trace['a1']['t2'],trace['a1']['prob']
- >>> x2, y2, prob2 = trace['t2']['t2'], trace['t2']['a1'],trace['t2']['prob']
- >>> plt.scatter(x, y, c=prob ,s=30)
- >>> plt.scatter(x2, y2, c=prob2, s=30)
- >>> plt.gca().set_xlim((1, 5))
- >>> plt.gca().set_ylim((5, 15))
- >>> plt.xlabel('a1')
- >>> plt.ylabel('t2')
- >>> plt.show()
-
-
-which shows the trace of values:
-
-.. image:: _images/conf_interval2.png
- :target: _images/conf_interval2.png
- :width: 50%
-
-
-
-Confidence Interval Functions
-----------------------------------
-
-.. autofunction:: lmfit.conf_interval
-
-.. autofunction:: lmfit.conf_interval2d
-
-.. autofunction:: lmfit.ci_report
+.. _confidence_chapter:
+
+Calculation of confidence intervals
+====================================
+
+.. module:: confidence
+
+The lmfit :mod:`confidence` module allows you to explicitly calculate
+confidence intervals for variable parameters. For most models, it is not
+necessary: the estimation of the standard error from the estimated
+covariance matrix is normally quite good.
+
+But for some models, e.g. a sum of two exponentials, the approximation
+begins to fail. For this case, lmfit has the function :func:`conf_interval`
+to calculate confidence intervals directly. This is substantially slower
+than using the errors estimated from the covariance matrix, but the results
+are more robust.
+
+
+Method used for calculating confidence intervals
+-------------------------------------------------
+
+The F-test is used to compare our null model, which is the best fit we have
+found, with an alternate model, where one of the parameters is fixed to a
+specific value. The value is changed until the difference between :math:`\chi^2_0`
+and :math:`\chi^2_{f}` can't be explained by the loss of a degree of freedom
+within a certain confidence.
+
+.. math::
+
+ F(P_{fix},N-P) = \left(\frac{\chi^2_f}{\chi^2_{0}}-1\right)\frac{N-P}{P_{fix}}
+
+N is the number of data-points, P the number of parameter of the null model.
+:math:`P_{fix}` is the number of fixed parameters (or to be more clear, the
+difference of number of parameters between our null model and the alternate
+model).
+
+Adding a log-likelihood method is under consideration.
+
+A basic example
+---------------
+
+First we create an example problem::
+
+ >>> import lmfit
+ >>> import numpy as np
+ >>> x = np.linspace(0.3,10,100)
+ >>> y = 1/(0.1*x)+2+0.1*np.random.randn(x.size)
+ >>> pars = lmfit.Parameters()
+ >>> pars.add_many(('a', 0.1), ('b', 1))
+ >>> def residual(p):
+ ... a = p['a'].value
+ ... b = p['b'].value
+ ... return 1/(a*x)+b-y
+
+
+before we can generate the confidence intervals, we have to run a fit, so
+that the automated estimate of the standard errors can be used as a
+starting point::
+
+
+ >>> mini = lmfit.Minimizer(residual, pars)
+ >>> result = mini.minimize()
+ >>> print(lmfit.fit_report(result.params))
+ [Variables]]
+ a: 0.09943895 +/- 0.000193 (0.19%) (init= 0.1)
+ b: 1.98476945 +/- 0.012226 (0.62%) (init= 1)
+ [[Correlations]] (unreported correlations are < 0.100)
+ C(a, b) = 0.601
+
+Now it is just a simple function call to calculate the confidence
+intervals::
+
+ >>> ci = lmfit.conf_interval(mini, result)
+ >>> lmfit.printfuncs.report_ci(ci)
+ 99.70% 95.00% 67.40% 0.00% 67.40% 95.00% 99.70%
+ a 0.09886 0.09905 0.09925 0.09944 0.09963 0.09982 0.10003
+ b 1.94751 1.96049 1.97274 1.97741 1.99680 2.00905 2.02203
+
+This shows the best-fit values for the parameters in the `0.00%` column,
+and parameter values that are at the varying confidence levels given by
+steps in :math:`\sigma`. As we can see, the estimated error is almost the
+same, and the uncertainties are well behaved: Going from 1 :math:`\sigma`
+(68% confidence) to 3 :math:`\sigma` (99.7% confidence) uncertainties is
+fairly linear. It can also be seen that the errors are fairy symmetric
+around the best fit value. For this problem, it is not necessary to
+calculate confidence intervals, and the estimates of the uncertainties from
+the covariance matrix are sufficient.
+
+An advanced example
+-------------------
+
+Now we look at a problem where calculating the error from approximated
+covariance can lead to misleading result -- two decaying exponentials. In
+fact such a problem is particularly hard for the Levenberg-Marquardt
+method, so we first estimate the results using the slower but robust
+Nelder-Mead method, and *then* use Levenberg-Marquardt to estimate the
+uncertainties and correlations
+
+
+.. literalinclude:: ../examples/doc_confidence2.py
+
+which will report::
+
+ [[Variables]]
+ a1: 2.98622120 +/- 0.148671 (4.98%) (init= 2.986237)
+ a2: -4.33526327 +/- 0.115275 (2.66%) (init=-4.335256)
+ t1: 1.30994233 +/- 0.131211 (10.02%) (init= 1.309932)
+ t2: 11.8240350 +/- 0.463164 (3.92%) (init= 11.82408)
+ [[Correlations]] (unreported correlations are < 0.500)
+ C(a2, t2) = 0.987
+ C(a2, t1) = -0.925
+ C(t1, t2) = -0.881
+ C(a1, t1) = -0.599
+ 95.00% 68.00% 0.00% 68.00% 95.00%
+ a1 2.71850 2.84525 2.98622 3.14874 3.34076
+ a2 -4.63180 -4.46663 -4.33526 -4.22883 -4.14178
+ t2 10.82699 11.33865 11.82404 12.28195 12.71094
+ t1 1.08014 1.18566 1.30994 1.45566 1.62579
+
+
+Again we called :func:`conf_interval`, this time with tracing and only for
+1- and 2 :math:`\sigma`. Comparing these two different estimates, we see
+that the estimate for `a1` is reasonably well approximated from the
+covariance matrix, but the estimates for `a2` and especially for `t1`, and
+`t2` are very asymmetric and that going from 1 :math:`\sigma` (68%
+confidence) to 2 :math:`\sigma` (95% confidence) is not very predictable.
+
+Let plots mad of the confidence region are shown the figure on the left
+below for ``a1`` and ``t2``, and for ``a2`` and ``t2`` on the right:
+
+.. _figC1:
+
+ .. image:: _images/conf_interval1.png
+ :target: _images/conf_interval1.png
+ :width: 48%
+ .. image:: _images/conf_interval1a.png
+ :target: _images/conf_interval1a.png
+ :width: 48%
+
+Neither of these plots is very much like an ellipse, which is implicitly
+assumed by the approach using the covariance matrix.
+
+The trace returned as the optional second argument from
+:func:`conf_interval` contains a dictionary for each variable parameter.
+The values are dictionaries with arrays of values for each variable, and an
+array of corresponding probabilities for the corresponding cumulative
+variables. This can be used to show the dependence between two
+parameters::
+
+ >>> x, y, prob = trace['a1']['a1'], trace['a1']['t2'],trace['a1']['prob']
+ >>> x2, y2, prob2 = trace['t2']['t2'], trace['t2']['a1'],trace['t2']['prob']
+ >>> plt.scatter(x, y, c=prob ,s=30)
+ >>> plt.scatter(x2, y2, c=prob2, s=30)
+ >>> plt.gca().set_xlim((1, 5))
+ >>> plt.gca().set_ylim((5, 15))
+ >>> plt.xlabel('a1')
+ >>> plt.ylabel('t2')
+ >>> plt.show()
+
+
+which shows the trace of values:
+
+.. image:: _images/conf_interval2.png
+ :target: _images/conf_interval2.png
+ :width: 50%
+
+The :meth:`Minimizer.emcee` method uses Markov Chain Monte Carlo to sample
+the posterior probability distribution. These distributions demonstrate the
+range of solutions that the data supports. The following image was obtained
+by using :meth:`Minimizer.emcee` on the same problem.
+
+.. image:: _images/emcee_triangle.png
+
+Credible intervals (the Bayesian equivalent of the frequentist confidence
+interval) can be obtained with this method. MCMC can be used for model
+selection, to determine outliers, to marginalise over nuisance parameters, etc.
+For example, you may have fractionally underestimated the uncertainties on a
+dataset. MCMC can be used to estimate the true level of uncertainty on each
+datapoint. A tutorial on the possibilities offered by MCMC can be found at [1]_.
+
+.. [1] http://jakevdp.github.io/blog/2014/03/11/frequentism-and-bayesianism-a-practical-intro/
+
+
+
+Confidence Interval Functions
+----------------------------------
+
+.. autofunction:: lmfit.conf_interval
+
+.. autofunction:: lmfit.conf_interval2d
+
+.. autofunction:: lmfit.ci_report
diff --git a/doc/constraints.rst b/doc/constraints.rst
index 8d7fc6e..7d06b8d 100644
--- a/doc/constraints.rst
+++ b/doc/constraints.rst
@@ -1,166 +1,166 @@
-.. _constraints_chapter:
-
-=================================
-Using Mathematical Constraints
-=================================
-
-.. _asteval: http://newville.github.io/asteval/
-
-Being able to fix variables to a constant value or place upper and lower
-bounds on their values can greatly simplify modeling real data. These
-capabilities are key to lmfit's Parameters. In addition, it is sometimes
-highly desirable to place mathematical constraints on parameter values.
-For example, one might want to require that two Gaussian peaks have the
-same width, or have amplitudes that are constrained to add to some value.
-Of course, one could rewrite the objective or model function to place such
-requirements, but this is somewhat error prone, and limits the flexibility
-so that exploring constraints becomes laborious.
-
-To simplify the setting of constraints, Parameters can be assigned a
-mathematical expression of other Parameters, builtin constants, and builtin
-mathematical functions that will be used to determine its value. The
-expressions used for constraints are evaluated using the `asteval`_ module,
-which uses Python syntax, and evaluates the constraint expressions in a safe
-and isolated namespace.
-
-This approach to mathematical constraints allows one to not have to write a
-separate model function for two Gaussians where the two ``sigma`` values are
-forced to be equal, or where amplitudes are related. Instead, one can write a
-more general two Gaussian model (perhaps using :class:`GaussianModel`) and
-impose such constraints on the Parameters for a particular fit.
-
-
-Overview
-===============
-
-Just as one can place bounds on a Parameter, or keep it fixed during the
-fit, so too can one place mathematical constraints on parameters. The way
-this is done with lmfit is to write a Parameter as a mathematical
-expression of the other parameters and a set of pre-defined operators and
-functions. The constraint expressions are simple Python statements,
-allowing one to place constraints like::
-
- pars = Parameters()
- pars.add('frac_curve1', value=0.5, min=0, max=1)
- pars.add('frac_curve2', expr='1-frac_curve1')
-
-as the value of the `frac_curve1` parameter is updated at each step in the
-fit, the value of `frac_curve2` will be updated so that the two values are
-constrained to add to 1.0. Of course, such a constraint could be placed in
-the fitting function, but the use of such constraints allows the end-user
-to modify the model of a more general-purpose fitting function.
-
-Nearly any valid mathematical expression can be used, and a variety of
-built-in functions are available for flexible modeling.
-
-Supported Operators, Functions, and Constants
-=================================================
-
-The mathematical expressions used to define constrained Parameters need to
-be valid python expressions. As you'd expect, the operators '+', '-', '*',
-'/', '**', are supported. In fact, a much more complete set can be used,
-including Python's bit- and logical operators::
-
- +, -, *, /, **, &, |, ^, <<, >>, %, and, or,
- ==, >, >=, <, <=, !=, ~, not, is, is not, in, not in
-
-
-The values for `e` (2.7182818...) and `pi` (3.1415926...) are available, as
-are several supported mathematical and trigonometric function::
-
- abs, acos, acosh, asin, asinh, atan, atan2, atanh, ceil,
- copysign, cos, cosh, degrees, exp, fabs, factorial,
- floor, fmod, frexp, fsum, hypot, isinf, isnan, ldexp,
- log, log10, log1p, max, min, modf, pow, radians, sin,
- sinh, sqrt, tan, tanh, trunc
-
-
-In addition, all Parameter names will be available in the mathematical
-expressions. Thus, with parameters for a few peak-like functions::
-
- pars = Parameters()
- pars.add('amp_1', value=0.5, min=0, max=1)
- pars.add('cen_1', value=2.2)
- pars.add('wid_1', value=0.2)
-
-The following expression are all valid::
-
- pars.add('amp_2', expr='(2.0 - amp_1**2)')
- pars.add('cen_2', expr='cen_1 * wid_2 / max(wid_1, 0.001)')
- pars.add('wid_2', expr='sqrt(pi)*wid_1')
-
-In fact, almost any valid Python expression is allowed. A notable example
-is that Python's 1-line *if expression* is supported::
-
- pars.add('bounded', expr='param_a if test_val/2. > 100 else param_b')
-
-which is equivalent to the more familiar::
-
- if test_val/2. > 100:
- bounded = param_a
- else:
- bounded = param_b
-
-Using Inequality Constraints
-==============================
-
-A rather common question about how to set up constraints
-that use an inequality, say, :math:`x + y \le 10`. This
-can be done with algebraic constraints by recasting the
-problem, as :math:`x + y = \delta` and :math:`\delta \le
-10`. That is, first, allow :math:`x` to be held by the
-freely varying parameter `x`. Next, define a parameter
-`delta` to be variable with a maximum value of 10, and
-define parameter `y` as `delta - x`::
-
- pars = Parameters()
- pars.add('x', value = 5, vary=True)
- pars.add('delta', value = 5, max=10, vary=True)
- pars.add('y', expr='delta-x')
-
-The essential point is that an inequality still implies
-that a variable (here, `delta`) is needed to describe the
-constraint. The secondary point is that upper and lower
-bounds can be used as part of the inequality to make the
-definitions more convenient.
-
-
-Advanced usage of Expressions in lmfit
-=============================================
-
-The expression used in a constraint is converted to a
-Python `Abstract Syntax Tree
-<http://docs.python.org/library/ast.html>`_, which is an
-intermediate version of the expression -- a syntax-checked,
-partially compiled expression. Among other things, this
-means that Python's own parser is used to parse and convert
-the expression into something that can easily be evaluated
-within Python. It also means that the symbols in the
-expressions can point to any Python object.
-
-In fact, the use of Python's AST allows a nearly full version of Python to
-be supported, without using Python's built-in :meth:`eval` function. The
-`asteval`_ module actually supports most Python syntax, including for- and
-while-loops, conditional expressions, and user-defined functions. There
-are several unsupported Python constructs, most notably the class
-statement, so that new classes cannot be created, and the import statement,
-which helps make the `asteval`_ module safe from malicious use.
-
-One important feature of the `asteval`_ module is that you can add
-domain-specific functions into the it, for later use in constraint
-expressions. To do this, you would use the :attr:`asteval` attribute of
-the :class:`Minimizer` class, which contains a complete AST interpreter.
-The `asteval`_ interpreter uses a flat namespace, implemented as a single
-dictionary. That means you can preload any Python symbol into the namespace
-for the constraints::
-
- def mylorentzian(x, amp, cen, wid):
- "lorentzian function: wid = half-width at half-max"
- return (amp / (1 + ((x-cen)/wid)**2))
-
- fitter = Minimizer()
- fitter.asteval.symtable['lorentzian'] = mylorentzian
-
-and this :meth:`lorentzian` function can now be used in constraint
-expressions.
-
+.. _constraints_chapter:
+
+=================================
+Using Mathematical Constraints
+=================================
+
+.. _asteval: http://newville.github.io/asteval/
+
+Being able to fix variables to a constant value or place upper and lower
+bounds on their values can greatly simplify modeling real data. These
+capabilities are key to lmfit's Parameters. In addition, it is sometimes
+highly desirable to place mathematical constraints on parameter values.
+For example, one might want to require that two Gaussian peaks have the
+same width, or have amplitudes that are constrained to add to some value.
+Of course, one could rewrite the objective or model function to place such
+requirements, but this is somewhat error prone, and limits the flexibility
+so that exploring constraints becomes laborious.
+
+To simplify the setting of constraints, Parameters can be assigned a
+mathematical expression of other Parameters, builtin constants, and builtin
+mathematical functions that will be used to determine its value. The
+expressions used for constraints are evaluated using the `asteval`_ module,
+which uses Python syntax, and evaluates the constraint expressions in a safe
+and isolated namespace.
+
+This approach to mathematical constraints allows one to not have to write a
+separate model function for two Gaussians where the two ``sigma`` values are
+forced to be equal, or where amplitudes are related. Instead, one can write a
+more general two Gaussian model (perhaps using :class:`GaussianModel`) and
+impose such constraints on the Parameters for a particular fit.
+
+
+Overview
+===============
+
+Just as one can place bounds on a Parameter, or keep it fixed during the
+fit, so too can one place mathematical constraints on parameters. The way
+this is done with lmfit is to write a Parameter as a mathematical
+expression of the other parameters and a set of pre-defined operators and
+functions. The constraint expressions are simple Python statements,
+allowing one to place constraints like::
+
+ pars = Parameters()
+ pars.add('frac_curve1', value=0.5, min=0, max=1)
+ pars.add('frac_curve2', expr='1-frac_curve1')
+
+as the value of the `frac_curve1` parameter is updated at each step in the
+fit, the value of `frac_curve2` will be updated so that the two values are
+constrained to add to 1.0. Of course, such a constraint could be placed in
+the fitting function, but the use of such constraints allows the end-user
+to modify the model of a more general-purpose fitting function.
+
+Nearly any valid mathematical expression can be used, and a variety of
+built-in functions are available for flexible modeling.
+
+Supported Operators, Functions, and Constants
+=================================================
+
+The mathematical expressions used to define constrained Parameters need to
+be valid python expressions. As you'd expect, the operators '+', '-', '*',
+'/', '**', are supported. In fact, a much more complete set can be used,
+including Python's bit- and logical operators::
+
+ +, -, *, /, **, &, |, ^, <<, >>, %, and, or,
+ ==, >, >=, <, <=, !=, ~, not, is, is not, in, not in
+
+
+The values for `e` (2.7182818...) and `pi` (3.1415926...) are available, as
+are several supported mathematical and trigonometric function::
+
+ abs, acos, acosh, asin, asinh, atan, atan2, atanh, ceil,
+ copysign, cos, cosh, degrees, exp, fabs, factorial,
+ floor, fmod, frexp, fsum, hypot, isinf, isnan, ldexp,
+ log, log10, log1p, max, min, modf, pow, radians, sin,
+ sinh, sqrt, tan, tanh, trunc
+
+
+In addition, all Parameter names will be available in the mathematical
+expressions. Thus, with parameters for a few peak-like functions::
+
+ pars = Parameters()
+ pars.add('amp_1', value=0.5, min=0, max=1)
+ pars.add('cen_1', value=2.2)
+ pars.add('wid_1', value=0.2)
+
+The following expression are all valid::
+
+ pars.add('amp_2', expr='(2.0 - amp_1**2)')
+ pars.add('cen_2', expr='cen_1 * wid_2 / max(wid_1, 0.001)')
+ pars.add('wid_2', expr='sqrt(pi)*wid_1')
+
+In fact, almost any valid Python expression is allowed. A notable example
+is that Python's 1-line *if expression* is supported::
+
+ pars.add('bounded', expr='param_a if test_val/2. > 100 else param_b')
+
+which is equivalent to the more familiar::
+
+ if test_val/2. > 100:
+ bounded = param_a
+ else:
+ bounded = param_b
+
+Using Inequality Constraints
+==============================
+
+A rather common question about how to set up constraints
+that use an inequality, say, :math:`x + y \le 10`. This
+can be done with algebraic constraints by recasting the
+problem, as :math:`x + y = \delta` and :math:`\delta \le
+10`. That is, first, allow :math:`x` to be held by the
+freely varying parameter `x`. Next, define a parameter
+`delta` to be variable with a maximum value of 10, and
+define parameter `y` as `delta - x`::
+
+ pars = Parameters()
+ pars.add('x', value = 5, vary=True)
+ pars.add('delta', value = 5, max=10, vary=True)
+ pars.add('y', expr='delta-x')
+
+The essential point is that an inequality still implies
+that a variable (here, `delta`) is needed to describe the
+constraint. The secondary point is that upper and lower
+bounds can be used as part of the inequality to make the
+definitions more convenient.
+
+
+Advanced usage of Expressions in lmfit
+=============================================
+
+The expression used in a constraint is converted to a
+Python `Abstract Syntax Tree
+<http://docs.python.org/library/ast.html>`_, which is an
+intermediate version of the expression -- a syntax-checked,
+partially compiled expression. Among other things, this
+means that Python's own parser is used to parse and convert
+the expression into something that can easily be evaluated
+within Python. It also means that the symbols in the
+expressions can point to any Python object.
+
+In fact, the use of Python's AST allows a nearly full version of Python to
+be supported, without using Python's built-in :meth:`eval` function. The
+`asteval`_ module actually supports most Python syntax, including for- and
+while-loops, conditional expressions, and user-defined functions. There
+are several unsupported Python constructs, most notably the class
+statement, so that new classes cannot be created, and the import statement,
+which helps make the `asteval`_ module safe from malicious use.
+
+One important feature of the `asteval`_ module is that you can add
+domain-specific functions into the it, for later use in constraint
+expressions. To do this, you would use the :attr:`asteval` attribute of
+the :class:`Minimizer` class, which contains a complete AST interpreter.
+The `asteval`_ interpreter uses a flat namespace, implemented as a single
+dictionary. That means you can preload any Python symbol into the namespace
+for the constraints::
+
+ def mylorentzian(x, amp, cen, wid):
+ "lorentzian function: wid = half-width at half-max"
+ return (amp / (1 + ((x-cen)/wid)**2))
+
+ fitter = Minimizer()
+ fitter.asteval.symtable['lorentzian'] = mylorentzian
+
+and this :meth:`lorentzian` function can now be used in constraint
+expressions.
+
diff --git a/doc/contents.rst b/doc/contents.rst
index 8a1e5c2..46c61b2 100644
--- a/doc/contents.rst
+++ b/doc/contents.rst
@@ -1,18 +1,18 @@
-Contents
-=================
-
-.. toctree::
- :maxdepth: 3
-
- intro
- installation
- whatsnew
- support
- faq
- parameters
- fitting
- model
- builtin_models
- confidence
- bounds
- constraints
+Contents
+=================
+
+.. toctree::
+ :maxdepth: 3
+
+ intro
+ installation
+ whatsnew
+ support
+ faq
+ parameters
+ fitting
+ model
+ builtin_models
+ confidence
+ bounds
+ constraints
diff --git a/doc/extensions.py b/doc/extensions.py
index 3e54c82..40de659 100644
--- a/doc/extensions.py
+++ b/doc/extensions.py
@@ -1,10 +1,10 @@
-# sphinx extensions for mathjax
-extensions = ['sphinx.ext.autodoc',
- 'sphinx.ext.todo',
- 'sphinx.ext.coverage',
- 'sphinx.ext.intersphinx',
- 'numpydoc']
-mathjax = 'sphinx.ext.mathjax'
-pngmath = 'sphinx.ext.pngmath'
-
-extensions.append(mathjax)
+# sphinx extensions for mathjax
+extensions = ['sphinx.ext.autodoc',
+ 'sphinx.ext.todo',
+ 'sphinx.ext.coverage',
+ 'sphinx.ext.intersphinx',
+ 'numpydoc']
+mathjax = 'sphinx.ext.mathjax'
+pngmath = 'sphinx.ext.pngmath'
+
+extensions.append(mathjax)
diff --git a/doc/extensions.pyc b/doc/extensions.pyc
index 4dfb438..2ea9e41 100644
Binary files a/doc/extensions.pyc and b/doc/extensions.pyc differ
diff --git a/doc/faq.rst b/doc/faq.rst
index f54dc88..1bf26f9 100644
--- a/doc/faq.rst
+++ b/doc/faq.rst
@@ -1,100 +1,95 @@
-.. _faq_chapter:
-
-====================================
-Frequently Asked Questions
-====================================
-
-A list of common questions.
-
-What's the best way to ask for help or submit a bug report?
-================================================================
-
-See :ref:`support_chapter`.
-
-
-Why did my script break when upgrading from lmfit 0.8.3 to 0.9.0?
-====================================================================
-
-See :ref:`whatsnew_090_label`
-
-
-I get import errors from IPython
-==============================================================
-
-If you see something like::
-
- from IPython.html.widgets import Dropdown
-
- ImportError: No module named 'widgets'
-
-then you need to install the ipywidgets package. Try 'pip install ipywidgets'.
-
-
-
-
-How can I fit multi-dimensional data?
-========================================
-
-The fitting routines accept data arrays that are 1 dimensional and double
-precision. So you need to convert the data and model (or the value
-returned by the objective function) to be one dimensional. A simple way to
-do this is to use numpy's :meth:`numpy.ndarray.flatten`, for example::
-
- def residual(params, x, data=None):
- ....
- resid = calculate_multidim_residual()
- return resid.flatten()
-
-How can I fit multiple data sets?
-========================================
-
-As above, the fitting routines accept data arrays that are 1 dimensional and double
-precision. So you need to convert the sets of data and models (or the value
-returned by the objective function) to be one dimensional. A simple way to
-do this is to use numpy's :meth:`numpy.concatenate`. As an example, here
-is a residual function to simultaneously fit two lines to two different
-arrays. As a bonus, the two lines share the 'offset' parameter:
-
- def fit_function(params, x=None, dat1=None, dat2=None):
- model1 = params['offset'].value + x * params['slope1'].value
- model2 = params['offset'].value + x * params['slope2'].value
-
- resid1 = dat1 - model1
- resid2 = dat2 - model2
- return numpy.concatenate((resid1, resid2))
-
-
-
-How can I fit complex data?
-===================================
-
-As with working with multidimensional data, you need to convert your data
-and model (or the value returned by the objective function) to be double precision
-floating point numbers. One way to do this would be to use a function like this::
-
- def realimag(array):
- return np.array([(x.real, x.imag) for x in array]).flatten()
-
-to convert the complex array into an array of alternating real and
-imaginary values. You can then use this function on the result returned by
-your objective function::
-
- def residual(params, x, data=None):
- ....
- resid = calculate_complex_residual()
- return realimag(resid)
-
-
-Can I constrain values to have integer values?
-===============================================
-
-Basically, no. None of the minimizers in lmfit support integer
-programming. They all (I think) assume that they can make a very small
-change to a floating point value for a parameters value and see a change in
-the value to be minimized.
-
-
-How should I cite LMFIT?
-==================================
-
-See http://dx.doi.org/10.5281/zenodo.11813
+.. _faq_chapter:
+
+====================================
+Frequently Asked Questions
+====================================
+
+A list of common questions.
+
+What's the best way to ask for help or submit a bug report?
+================================================================
+
+See :ref:`support_chapter`.
+
+
+Why did my script break when upgrading from lmfit 0.8.3 to 0.9.0?
+====================================================================
+
+See :ref:`whatsnew_090_label`
+
+
+I get import errors from IPython
+==============================================================
+
+If you see something like::
+
+ from IPython.html.widgets import Dropdown
+
+ ImportError: No module named 'widgets'
+
+then you need to install the ipywidgets package. Try 'pip install ipywidgets'.
+
+
+
+
+How can I fit multi-dimensional data?
+========================================
+
+The fitting routines accept data arrays that are 1 dimensional and double
+precision. So you need to convert the data and model (or the value
+returned by the objective function) to be one dimensional. A simple way to
+do this is to use numpy's :numpydoc:`ndarray.flatten`, for example::
+
+ def residual(params, x, data=None):
+ ....
+ resid = calculate_multidim_residual()
+ return resid.flatten()
+
+How can I fit multiple data sets?
+========================================
+
+As above, the fitting routines accept data arrays that are 1 dimensional
+and double precision. So you need to convert the sets of data and models
+(or the value returned by the objective function) to be one dimensional. A
+simple way to do this is to use numpy's :numpydoc:`concatenate`. As an
+example, here is a residual function to simultaneously fit two lines to two
+different arrays. As a bonus, the two lines share the 'offset' parameter::
+
+ def fit_function(params, x=None, dat1=None, dat2=None):
+ model1 = params['offset'].value + x * params['slope1'].value
+ model2 = params['offset'].value + x * params['slope2'].value
+
+ resid1 = dat1 - model1
+ resid2 = dat2 - model2
+ return numpy.concatenate((resid1, resid2))
+
+
+
+How can I fit complex data?
+===================================
+
+As with working with multidimensional data, you need to convert your data
+and model (or the value returned by the objective function) to be double
+precision floating point numbers. The simplest approach is to use numpy's
+:numpydoc:`ndarray.view` method, perhaps like::
+
+ import numpy as np
+ def residual(params, x, data=None):
+ ....
+ resid = calculate_complex_residual()
+ return resid.view(np.float)
+
+
+Can I constrain values to have integer values?
+===============================================
+
+Basically, no. None of the minimizers in lmfit support integer
+programming. They all (I think) assume that they can make a very small
+change to a floating point value for a parameters value and see a change in
+the value to be minimized.
+
+
+How should I cite LMFIT?
+==================================
+
+See http://dx.doi.org/10.5281/zenodo.11813
diff --git a/doc/fitting.rst b/doc/fitting.rst
index f07ce77..cde5d89 100644
--- a/doc/fitting.rst
+++ b/doc/fitting.rst
@@ -1,619 +1,900 @@
-.. _minimize_chapter:
-
-=======================================
-Performing Fits, Analyzing Outputs
-=======================================
-
-As shown in the previous chapter, a simple fit can be performed with the
-:func:`minimize` function. For more sophisticated modeling, the
-:class:`Minimizer` class can be used to gain a bit more control, especially
-when using complicated constraints or comparing results from related fits.
-
-
-.. warning::
-
- Upgrading scripts from version 0.8.3 to 0.9.0? See :ref:`whatsnew_090_label`
-
-
-The :func:`minimize` function
-===============================
-
-The :func:`minimize` function is a wrapper around :class:`Minimizer` for
-running an optimization problem. It takes an objective function (the
-function that calculates the array to be minimized), a :class:`Parameters`
-object, and several optional arguments. See :ref:`fit-func-label` for
-details on writing the objective.
-
-.. function:: minimize(function, params[, args=None[, kws=None[, method='leastsq'[, scale_covar=True[, iter_cb=None[, **fit_kws]]]]]])
-
- find values for the ``params`` so that the sum-of-squares of the array returned
- from ``function`` is minimized.
-
- :param function: function to return fit residual. See :ref:`fit-func-label` for details.
- :type function: callable.
- :param params: a :class:`Parameters` dictionary. Keywords must be strings
- that match ``[a-z_][a-z0-9_]*`` and cannot be a python
- reserved word. Each value must be :class:`Parameter`.
- :type params: :class:`Parameters`.
- :param args: arguments tuple to pass to the residual function as positional arguments.
- :type args: tuple
- :param kws: dictionary to pass to the residual function as keyword arguments.
- :type kws: dict
- :param method: name of fitting method to use. See :ref:`fit-methods-label` for details
- :type method: string (default ``leastsq``)
- :param scale_covar: whether to automatically scale covariance matrix (``leastsq`` only)
- :type scale_covar: bool (default ``True``)
- :param iter_cb: function to be called at each fit iteration. See :ref:`fit-itercb-label` for details.
- :type iter_cb: callable or ``None``
- :param fit_kws: dictionary to pass to :func:`scipy.optimize.leastsq` or :func:`scipy.optimize.minimize`.
- :type fit_kws: dict
-
- :return: :class:`MinimizerResult` instance, which will contain the
- optimized parameter, and several goodness-of-fit statistics.
-
-.. versionchanged:: 0.9.0
- return value changed to :class:`MinimizerResult`
-
-
- On output, the params will be unchanged. The best-fit values, and where
- appropriate, estimated uncertainties and correlations, will all be
- contained in the returned :class:`MinimizerResult`. See
- :ref:`fit-results-label` for further details.
-
- For clarity, it should be emphasized that this function is simply a
- wrapper around :class:`Minimizer` that runs a single fit, implemented as::
-
- fitter = Minimizer(fcn, params, fcn_args=args, fcn_kws=kws,
- iter_cb=iter_cb, scale_covar=scale_covar, **fit_kws)
- return fitter.minimize(method=method)
-
-
-.. _fit-func-label:
-
-
-Writing a Fitting Function
-===============================
-
-An important component of a fit is writing a function to be minimized --
-the *objective function*. Since this function will be called by other
-routines, there are fairly stringent requirements for its call signature
-and return value. In principle, your function can be any python callable,
-but it must look like this:
-
-.. function:: func(params, *args, **kws):
-
- calculate objective residual to be minimized from parameters.
-
- :param params: parameters.
- :type params: :class:`Parameters`.
- :param args: positional arguments. Must match ``args`` argument to :func:`minimize`
- :param kws: keyword arguments. Must match ``kws`` argument to :func:`minimize`
- :return: residual array (generally data-model) to be minimized in the least-squares sense.
- :rtype: numpy array. The length of this array cannot change between calls.
-
-
-A common use for the positional and keyword arguments would be to pass in other
-data needed to calculate the residual, including such things as the data array,
-dependent variable, uncertainties in the data, and other data structures for the
-model calculation.
-
-The objective function should return the value to be minimized. For the
-Levenberg-Marquardt algorithm from :meth:`leastsq`, this returned value **must** be an
-array, with a length greater than or equal to the number of fitting variables in the
-model. For the other methods, the return value can either be a scalar or an array. If an
-array is returned, the sum of squares of the array will be sent to the underlying fitting
-method, effectively doing a least-squares optimization of the return values.
-
-
-Since the function will be passed in a dictionary of :class:`Parameters`, it is advisable
-to unpack these to get numerical values at the top of the function. A
-simple way to do this is with :meth:`Parameters.valuesdict`, as with::
-
-
- def residual(pars, x, data=None, eps=None):
- # unpack parameters:
- # extract .value attribute for each parameter
- parvals = pars.valuesdict()
- period = parvals['period']
- shift = parvals['shift']
- decay = parvals['decay']
-
- if abs(shift) > pi/2:
- shift = shift - sign(shift)*pi
-
- if abs(period) < 1.e-10:
- period = sign(period)*1.e-10
-
- model = parvals['amp'] * sin(shift + x/period) * exp(-x*x*decay*decay)
-
- if data is None:
- return model
- if eps is None:
- return (model - data)
- return (model - data)/eps
-
-In this example, ``x`` is a positional (required) argument, while the
-``data`` array is actually optional (so that the function returns the model
-calculation if the data is neglected). Also note that the model
-calculation will divide ``x`` by the value of the 'period' Parameter. It
-might be wise to ensure this parameter cannot be 0. It would be possible
-to use the bounds on the :class:`Parameter` to do this::
-
- params['period'] = Parameter(value=2, min=1.e-10)
-
-but putting this directly in the function with::
-
- if abs(period) < 1.e-10:
- period = sign(period)*1.e-10
-
-is also a reasonable approach. Similarly, one could place bounds on the
-``decay`` parameter to take values only between ``-pi/2`` and ``pi/2``.
-
-.. _fit-methods-label:
-
-Choosing Different Fitting Methods
-===========================================
-
-By default, the `Levenberg-Marquardt
-<http://en.wikipedia.org/wiki/Levenberg-Marquardt_algorithm>`_ algorithm is
-used for fitting. While often criticized, including the fact it finds a
-*local* minima, this approach has some distinct advantages. These include
-being fast, and well-behaved for most curve-fitting needs, and making it
-easy to estimate uncertainties for and correlations between pairs of fit
-variables, as discussed in :ref:`fit-results-label`.
-
-Alternative algorithms can also be used by providing the ``method``
-keyword to the :func:`minimize` function or :meth:`Minimizer.minimize`
-class as listed in the :ref:`Table of Supported Fitting Methods
-<fit-methods-table>`.
-
-.. _fit-methods-table:
-
- Table of Supported Fitting Method, eithers:
-
- +-----------------------+------------------------------------------------------------------+
- | Fitting Method | ``method`` arg to :func:`minimize` or :meth:`Minimizer.minimize` |
- +=======================+==================================================================+
- | Levenberg-Marquardt | ``leastsq`` |
- +-----------------------+------------------------------------------------------------------+
- | Nelder-Mead | ``nelder`` |
- +-----------------------+------------------------------------------------------------------+
- | L-BFGS-B | ``lbfgsb`` |
- +-----------------------+------------------------------------------------------------------+
- | Powell | ``powell`` |
- +-----------------------+------------------------------------------------------------------+
- | Conjugate Gradient | ``cg`` |
- +-----------------------+------------------------------------------------------------------+
- | Newton-CG | ``newton`` |
- +-----------------------+------------------------------------------------------------------+
- | COBYLA | ``cobyla`` |
- +-----------------------+------------------------------------------------------------------+
- | Truncated Newton | ``tnc`` |
- +-----------------------+------------------------------------------------------------------+
- | Dogleg | ``dogleg`` |
- +-----------------------+------------------------------------------------------------------+
- | Sequential Linear | ``slsqp`` |
- | Squares Programming | |
- +-----------------------+------------------------------------------------------------------+
- | Differential | ``differential_evolution`` |
- | Evolution | |
- +-----------------------+------------------------------------------------------------------+
-
-
-.. note::
-
- The objective function for the Levenberg-Marquardt method **must**
- return an array, with more elements than variables. All other methods
- can return either a scalar value or an array.
-
-
-.. warning::
-
- Much of this documentation assumes that the Levenberg-Marquardt method is
- the method used. Many of the fit statistics and estimates for
- uncertainties in parameters discussed in :ref:`fit-results-label` are
- done only for this method.
-
-
-.. _fit-results-label:
-
-:class:`MinimizerResult` -- the optimization result
-========================================================
-
-
-
-.. class:: MinimizerResult(**kws)
-
-.. versionadded:: 0.9.0
-
-An optimization with :func:`minimize` or :meth:`Minimizer.minimize`
-will return a :class:`MinimizerResult` object. This is an otherwise
-plain container object (that is, with no methods of its own) that
-simply holds the results of the minimization. These results will
-include several pieces of informational data such as status and error
-messages, fit statistics, and the updated parameters themselves.
-
-Importantly, the parameters passed in to :meth:`Minimizer.minimize`
-will be not be changed. To to find the best-fit values, uncertainties
-and so on for each parameter, one must use the
-:attr:`MinimizerResult.params` attribute.
-
-.. attribute:: params
-
- the :class:`Parameters` actually used in the fit, with updated
- values, :attr:`stderr` and :attr:`correl`.
-
-.. attribute:: var_names
-
- ordered list of variable parameter names used in optimization, and
- useful for understanding the the values in :attr:`init_vals` and
- :attr:`covar`.
-
-.. attribute:: covar
-
- covariance matrix from minimization (`leastsq` only), with
- rows/columns using :attr:`var_names`.
-
-.. attribute:: init_vals
-
- list of initial values for variable parameters using :attr:`var_names`.
-
-.. attribute:: nfev
-
- number of function evaluations
-
-.. attribute:: success
-
- boolean (``True``/``False``) for whether fit succeeded.
-
-.. attribute:: errorbars
-
- boolean (``True``/``False``) for whether uncertainties were
- estimated.
-
-.. attribute:: message
-
- message about fit success.
-
-.. attribute:: ier
-
- integer error value from :func:`scipy.optimize.leastsq` (`leastsq`
- only).
-
-.. attribute:: lmdif_message
-
- message from :func:`scipy.optimize.leastsq` (`leastsq` only).
-
-
-.. attribute:: nvarys
-
- number of variables in fit :math:`N_{\rm varys}`
-
-.. attribute:: ndata
-
- number of data points: :math:`N`
-
-.. attribute:: nfree `
-
- degrees of freedom in fit: :math:`N - N_{\rm varys}`
-
-.. attribute:: residual
-
- residual array, return value of :func:`func`: :math:`{\rm Resid}`
-
-.. attribute:: chisqr
-
- chi-square: :math:`\chi^2 = \sum_i^N [{\rm Resid}_i]^2`
-
-.. attribute:: redchi
-
- reduced chi-square: :math:`\chi^2_{\nu}= {\chi^2} / {(N - N_{\rm
- varys})}`
-
-.. attribute:: aic
-
- Akaike Information Criterion statistic (see below)
-
-.. attribute:: bic
-
- Bayesian Information Criterion statistic (see below).
-
-
-
-
-
-Goodness-of-Fit Statistics
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. _goodfit-table:
-
- Table of Fit Results: These values, including the standard Goodness-of-Fit statistics,
- are all attributes of the :class:`MinimizerResult` object returned by
- :func:`minimize` or :meth:`Minimizer.minimize`.
-
-+----------------------+----------------------------------------------------------------------------+
-| Attribute Name | Description / Formula |
-+======================+============================================================================+
-| nfev | number of function evaluations |
-+----------------------+----------------------------------------------------------------------------+
-| nvarys | number of variables in fit :math:`N_{\rm varys}` |
-+----------------------+----------------------------------------------------------------------------+
-| ndata | number of data points: :math:`N` |
-+----------------------+----------------------------------------------------------------------------+
-| nfree ` | degrees of freedom in fit: :math:`N - N_{\rm varys}` |
-+----------------------+----------------------------------------------------------------------------+
-| residual | residual array, return value of :func:`func`: :math:`{\rm Resid}` |
-+----------------------+----------------------------------------------------------------------------+
-| chisqr | chi-square: :math:`\chi^2 = \sum_i^N [{\rm Resid}_i]^2` |
-+----------------------+----------------------------------------------------------------------------+
-| redchi | reduced chi-square: :math:`\chi^2_{\nu}= {\chi^2} / {(N - N_{\rm varys})}` |
-+----------------------+----------------------------------------------------------------------------+
-| aic | Akaike Information Criterion statistic (see below) |
-+----------------------+----------------------------------------------------------------------------+
-| bic | Bayesian Information Criterion statistic (see below) |
-+----------------------+----------------------------------------------------------------------------+
-| var_names | ordered list of variable parameter names used for init_vals and covar |
-+----------------------+----------------------------------------------------------------------------+
-| covar | covariance matrix (with rows/columns using var_names |
-+----------------------+----------------------------------------------------------------------------+
-| init_vals | list of initial values for variable parameters |
-+----------------------+----------------------------------------------------------------------------+
-
-Note that the calculation of chi-square and reduced chi-square assume
-that the returned residual function is scaled properly to the
-uncertainties in the data. For these statistics to be meaningful, the
-person writing the function to be minimized must scale them properly.
-
-After a fit using using the :meth:`leastsq` method has completed
-successfully, standard errors for the fitted variables and correlations
-between pairs of fitted variables are automatically calculated from the
-covariance matrix. The standard error (estimated :math:`1\sigma`
-error-bar) go into the :attr:`stderr` attribute of the Parameter. The
-correlations with all other variables will be put into the
-:attr:`correl` attribute of the Parameter -- a dictionary with keys for
-all other Parameters and values of the corresponding correlation.
-
-In some cases, it may not be possible to estimate the errors and
-correlations. For example, if a variable actually has no practical effect
-on the fit, it will likely cause the covariance matrix to be singular,
-making standard errors impossible to estimate. Placing bounds on varied
-Parameters makes it more likely that errors cannot be estimated, as being
-near the maximum or minimum value makes the covariance matrix singular. In
-these cases, the :attr:`errorbars` attribute of the fit result
-(:class:`Minimizer` object) will be ``False``.
-
-Akaike and Bayesian Information Criteria
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-The :class:`MinimizerResult` includes the tradtional chi-square and reduced chi-square statistics:
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- \chi^2 &=& \sum_i^N r_i^2 \\
- \chi^2_\nu &=& = \chi^2 / (N-N_{\rm varys})
- \end{eqnarray*}
-
-where :math:`r` is the residual array returned by the objective function
-(likely to be ``(data-model)/uncertainty`` for data modeling usages),
-:math:`N` is the number of data points (``ndata``), and :math:`N_{\rm
-varys}` is number of variable parameters.
-
-Also included are the `Akaike Information Criterion
-<http://en.wikipedia.org/wiki/Akaike_information_criterion>`_, and
-`Bayesian Information Criterion
-<http://en.wikipedia.org/wiki/Bayesian_information_criterion>`_ statistics,
-held in the ``aic`` and ``bic`` attributes, respectively. These give slightly
-different measures of the relative quality for a fit, trying to balance
-quality of fit with the number of variable parameters used in the fit.
-These are calculated as
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- {\rm aic} &=& N \ln(\chi^2/N) + 2 N_{\rm varys} \\
- {\rm bic} &=& N \ln(\chi^2/N) + \ln(N) *N_{\rm varys} \\
- \end{eqnarray*}
-
-
-When comparing fits with different numbers of varying parameters, one
-typically selects the model with lowest reduced chi-square, Akaike
-information criterion, and/or Bayesian information criterion. Generally,
-the Bayesian information criterion is considered the most conservative of
-these statistics.
-
-.. _fit-itercb-label:
-
-
-Using a Iteration Callback Function
-====================================
-
-An iteration callback function is a function to be called at each
-iteration, just after the objective function is called. The iteration
-callback allows user-supplied code to be run at each iteration, and can be
-used to abort a fit.
-
-.. function:: iter_cb(params, iter, resid, *args, **kws):
-
- user-supplied function to be run at each iteration
-
- :param params: parameters.
- :type params: :class:`Parameters`.
- :param iter: iteration number
- :type iter: integer
- :param resid: residual array.
- :type resid: ndarray
- :param args: positional arguments. Must match ``args`` argument to :func:`minimize`
- :param kws: keyword arguments. Must match ``kws`` argument to :func:`minimize`
- :return: residual array (generally data-model) to be minimized in the least-squares sense.
- :rtype: ``None`` for normal behavior, any value like ``True`` to abort fit.
-
-
-Normally, the iteration callback would have no return value or return
-``None``. To abort a fit, have this function return a value that is
-``True`` (including any non-zero integer). The fit will also abort if any
-exception is raised in the iteration callback. When a fit is aborted this
-way, the parameters will have the values from the last iteration. The fit
-statistics are not likely to be meaningful, and uncertainties will not be computed.
-
-
-.. module:: Minimizer
-
-.. _fit-minimizer-label:
-
-Using the :class:`Minimizer` class
-=======================================
-
-For full control of the fitting process, you'll want to create a
-:class:`Minimizer` object.
-
-.. class:: Minimizer(function, params, fcn_args=None, fcn_kws=None, iter_cb=None, scale_covar=True, **kws)
-
- creates a Minimizer, for more detailed access to fitting methods and attributes.
-
- :param function: objective function to return fit residual. See :ref:`fit-func-label` for details.
- :type function: callable.
- :param params: a dictionary of Parameters. Keywords must be strings
- that match ``[a-z_][a-z0-9_]*`` and is not a python
- reserved word. Each value must be :class:`Parameter`.
- :type params: dict
- :param fcn_args: arguments tuple to pass to the residual function as positional arguments.
- :type fcn_args: tuple
- :param fcn_kws: dictionary to pass to the residual function as keyword arguments.
- :type fcn_kws: dict
- :param iter_cb: function to be called at each fit iteration. See :ref:`fit-itercb-label` for details.
- :type iter_cb: callable or ``None``
- :param scale_covar: flag for automatically scaling covariance matrix and uncertainties to reduced chi-square (``leastsq`` only)
- :type scale_cover: bool (default ``True``).
- :param kws: dictionary to pass as keywords to the underlying :mod:`scipy.optimize` method.
- :type kws: dict
-
-The Minimizer object has a few public methods:
-
-.. method:: minimize(method='leastsq', params=None, **kws)
-
- perform fit using either :meth:`leastsq` or :meth:`scalar_minimize`.
-
- :param method: name of fitting method. Must be one of the naemes in
- :ref:`Table of Supported Fitting Methods <fit-methods-table>`
- :type method: str.
- :param params: a :class:`Parameters` dictionary for starting values
- :type params: :class:`Parameters` or `None`
-
- :return: :class:`MinimizerResult` object, containing updated
- parameters, fitting statistics, and information.
-
-.. versionchanged:: 0.9.0
- return value changed to :class:`MinimizerResult`
-
- Additonal keywords are passed on to the correspond :meth:`leastsq`
- or :meth:`scalar_minimize` method.
-
-
-.. method:: leastsq(params=None, scale_covar=True, **kws)
-
- perform fit with Levenberg-Marquardt algorithm. Keywords will be
- passed directly to :func:`scipy.optimize.leastsq`. By default,
- numerical derivatives are used, and the following arguments are set:
-
-
- +------------------+----------------+------------------------------------------------------------+
- | :meth:`leastsq` | Default Value | Description |
- | arg | | |
- +==================+================+============================================================+
- | xtol | 1.e-7 | Relative error in the approximate solution |
- +------------------+----------------+------------------------------------------------------------+
- | ftol | 1.e-7 | Relative error in the desired sum of squares |
- +------------------+----------------+------------------------------------------------------------+
- | maxfev | 2000*(nvar+1) | maximum number of function calls (nvar= # of variables) |
- +------------------+----------------+------------------------------------------------------------+
- | Dfun | ``None`` | function to call for Jacobian calculation |
- +------------------+----------------+------------------------------------------------------------+
-
-
-.. versionchanged:: 0.9.0
- return value changed to :class:`MinimizerResult`
-
-.. method:: scalar_minimize(method='Nelder-Mead', params=None, hess=None, tol=None, **kws)
-
- perform fit with any of the scalar minimization algorithms supported by
- :func:`scipy.optimize.minimize`.
-
- +-------------------------+-----------------+-----------------------------------------------------+
- | :meth:`scalar_minimize` | Default Value | Description |
- | arg | | |
- +=========================+=================+=====================================================+
- | method | ``Nelder-Mead`` | fitting method |
- +-------------------------+-----------------+-----------------------------------------------------+
- | tol | 1.e-7 | fitting and parameter tolerance |
- +-------------------------+-----------------+-----------------------------------------------------+
- | hess | None | Hessian of objective function |
- +-------------------------+-----------------+-----------------------------------------------------+
-
-.. versionchanged:: 0.9.0
- return value changed to :class:`MinimizerResult`
-
-.. method:: prepare_fit(**kws)
-
- prepares and initializes model and Parameters for subsequent
- fitting. This routine prepares the conversion of :class:`Parameters`
- into fit variables, organizes parameter bounds, and parses, "compiles"
- and checks constrain expressions. The method also creates and returns
- a new instance of a :class:`MinimizerResult` object that contains the
- copy of the Parameters that will actually be varied in the fit.
-
- This method is called directly by the fitting methods, and it is
- generally not necessary to call this function explicitly.
-
-.. versionchanged:: 0.9.0
- return value changed to :class:`MinimizerResult`
-
-
-
-Getting and Printing Fit Reports
-===========================================
-
-.. function:: fit_report(result, modelpars=None, show_correl=True, min_correl=0.1)
-
- generate and return text of report of best-fit values, uncertainties,
- and correlations from fit.
-
- :param result: :class:`MinimizerResult` object as returned by :func:`minimize`.
- :param modelpars: Parameters with "Known Values" (optional, default None)
- :param show_correl: whether to show list of sorted correlations [``True``]
- :param min_correl: smallest correlation absolute value to show [0.1]
-
- If the first argument is a :class:`Parameters` object,
- goodness-of-fit statistics will not be included.
-
-.. function:: report_fit(result, modelpars=None, show_correl=True, min_correl=0.1)
-
- print text of report from :func:`fit_report`.
-
-
-An example fit with report would be
-
-.. literalinclude:: ../examples/doc_withreport.py
-
-which would write out::
-
- [[Fit Statistics]]
- # function evals = 85
- # data points = 1001
- # variables = 4
- chi-square = 498.812
- reduced chi-square = 0.500
- [[Variables]]
- amp: 13.9121944 +/- 0.141202 (1.01%) (init= 13)
- period: 5.48507044 +/- 0.026664 (0.49%) (init= 2)
- shift: 0.16203677 +/- 0.014056 (8.67%) (init= 0)
- decay: 0.03264538 +/- 0.000380 (1.16%) (init= 0.02)
- [[Correlations]] (unreported correlations are < 0.100)
- C(period, shift) = 0.797
- C(amp, decay) = 0.582
- C(amp, shift) = -0.297
- C(amp, period) = -0.243
- C(shift, decay) = -0.182
- C(period, decay) = -0.150
+.. _minimize_chapter:
+
+=======================================
+Performing Fits, Analyzing Outputs
+=======================================
+
+As shown in the previous chapter, a simple fit can be performed with the
+:func:`minimize` function. For more sophisticated modeling, the
+:class:`Minimizer` class can be used to gain a bit more control, especially
+when using complicated constraints or comparing results from related fits.
+
+.. warning::
+
+ Upgrading scripts from version 0.8.3 to 0.9.0? See :ref:`whatsnew_090_label`
+
+
+The :func:`minimize` function
+===============================
+
+The :func:`minimize` function is a wrapper around :class:`Minimizer` for
+running an optimization problem. It takes an objective function (the
+function that calculates the array to be minimized), a :class:`Parameters`
+object, and several optional arguments. See :ref:`fit-func-label` for
+details on writing the objective.
+
+.. function:: minimize(function, params[, args=None[, kws=None[, method='leastsq'[, scale_covar=True[, iter_cb=None[, **fit_kws]]]]]])
+
+ find values for the ``params`` so that the sum-of-squares of the array returned
+ from ``function`` is minimized.
+
+ :param function: function to return fit residual. See :ref:`fit-func-label` for details.
+ :type function: callable.
+ :param params: a :class:`Parameters` dictionary. Keywords must be strings
+ that match ``[a-z_][a-z0-9_]*`` and cannot be a python
+ reserved word. Each value must be :class:`Parameter`.
+ :type params: :class:`Parameters`.
+ :param args: arguments tuple to pass to the residual function as positional arguments.
+ :type args: tuple
+ :param kws: dictionary to pass to the residual function as keyword arguments.
+ :type kws: dict
+ :param method: name of fitting method to use. See :ref:`fit-methods-label` for details
+ :type method: string (default ``leastsq``)
+ :param scale_covar: whether to automatically scale covariance matrix (``leastsq`` only)
+ :type scale_covar: bool (default ``True``)
+ :param iter_cb: function to be called at each fit iteration. See :ref:`fit-itercb-label` for details.
+ :type iter_cb: callable or ``None``
+ :param fit_kws: dictionary to pass to :scipydoc:`optimize.leastsq` or :scipydoc:`optimize.minimize`.
+ :type fit_kws: dict
+
+ :return: :class:`MinimizerResult` instance, which will contain the
+ optimized parameter, and several goodness-of-fit statistics.
+
+.. versionchanged:: 0.9.0
+ return value changed to :class:`MinimizerResult`
+
+
+ On output, the params will be unchanged. The best-fit values, and where
+ appropriate, estimated uncertainties and correlations, will all be
+ contained in the returned :class:`MinimizerResult`. See
+ :ref:`fit-results-label` for further details.
+
+ For clarity, it should be emphasized that this function is simply a
+ wrapper around :class:`Minimizer` that runs a single fit, implemented as::
+
+ fitter = Minimizer(fcn, params, fcn_args=args, fcn_kws=kws,
+ iter_cb=iter_cb, scale_covar=scale_covar, **fit_kws)
+ return fitter.minimize(method=method)
+
+
+.. _fit-func-label:
+
+
+Writing a Fitting Function
+===============================
+
+An important component of a fit is writing a function to be minimized --
+the *objective function*. Since this function will be called by other
+routines, there are fairly stringent requirements for its call signature
+and return value. In principle, your function can be any python callable,
+but it must look like this:
+
+.. function:: func(params, *args, **kws):
+
+ calculate objective residual to be minimized from parameters.
+
+ :param params: parameters.
+ :type params: :class:`Parameters`.
+ :param args: positional arguments. Must match ``args`` argument to :func:`minimize`
+ :param kws: keyword arguments. Must match ``kws`` argument to :func:`minimize`
+ :return: residual array (generally data-model) to be minimized in the least-squares sense.
+ :rtype: numpy array. The length of this array cannot change between calls.
+
+
+A common use for the positional and keyword arguments would be to pass in other
+data needed to calculate the residual, including such things as the data array,
+dependent variable, uncertainties in the data, and other data structures for the
+model calculation.
+
+The objective function should return the value to be minimized. For the
+Levenberg-Marquardt algorithm from :meth:`leastsq`, this returned value **must** be an
+array, with a length greater than or equal to the number of fitting variables in the
+model. For the other methods, the return value can either be a scalar or an array. If an
+array is returned, the sum of squares of the array will be sent to the underlying fitting
+method, effectively doing a least-squares optimization of the return values.
+
+
+Since the function will be passed in a dictionary of :class:`Parameters`, it is advisable
+to unpack these to get numerical values at the top of the function. A
+simple way to do this is with :meth:`Parameters.valuesdict`, as with::
+
+
+ def residual(pars, x, data=None, eps=None):
+ # unpack parameters:
+ # extract .value attribute for each parameter
+ parvals = pars.valuesdict()
+ period = parvals['period']
+ shift = parvals['shift']
+ decay = parvals['decay']
+
+ if abs(shift) > pi/2:
+ shift = shift - sign(shift)*pi
+
+ if abs(period) < 1.e-10:
+ period = sign(period)*1.e-10
+
+ model = parvals['amp'] * sin(shift + x/period) * exp(-x*x*decay*decay)
+
+ if data is None:
+ return model
+ if eps is None:
+ return (model - data)
+ return (model - data)/eps
+
+In this example, ``x`` is a positional (required) argument, while the
+``data`` array is actually optional (so that the function returns the model
+calculation if the data is neglected). Also note that the model
+calculation will divide ``x`` by the value of the 'period' Parameter. It
+might be wise to ensure this parameter cannot be 0. It would be possible
+to use the bounds on the :class:`Parameter` to do this::
+
+ params['period'] = Parameter(value=2, min=1.e-10)
+
+but putting this directly in the function with::
+
+ if abs(period) < 1.e-10:
+ period = sign(period)*1.e-10
+
+is also a reasonable approach. Similarly, one could place bounds on the
+``decay`` parameter to take values only between ``-pi/2`` and ``pi/2``.
+
+.. _fit-methods-label:
+
+Choosing Different Fitting Methods
+===========================================
+
+By default, the `Levenberg-Marquardt
+<http://en.wikipedia.org/wiki/Levenberg-Marquardt_algorithm>`_ algorithm is
+used for fitting. While often criticized, including the fact it finds a
+*local* minima, this approach has some distinct advantages. These include
+being fast, and well-behaved for most curve-fitting needs, and making it
+easy to estimate uncertainties for and correlations between pairs of fit
+variables, as discussed in :ref:`fit-results-label`.
+
+Alternative algorithms can also be used by providing the ``method``
+keyword to the :func:`minimize` function or :meth:`Minimizer.minimize`
+class as listed in the :ref:`Table of Supported Fitting Methods
+<fit-methods-table>`.
+
+.. _fit-methods-table:
+
+ Table of Supported Fitting Methods:
+
+ +-----------------------+------------------------------------------------------------------+
+ | Fitting Method | ``method`` arg to :func:`minimize` or :meth:`Minimizer.minimize` |
+ +=======================+==================================================================+
+ | Levenberg-Marquardt | ``leastsq`` |
+ +-----------------------+------------------------------------------------------------------+
+ | Nelder-Mead | ``nelder`` |
+ +-----------------------+------------------------------------------------------------------+
+ | L-BFGS-B | ``lbfgsb`` |
+ +-----------------------+------------------------------------------------------------------+
+ | Powell | ``powell`` |
+ +-----------------------+------------------------------------------------------------------+
+ | Conjugate Gradient | ``cg`` |
+ +-----------------------+------------------------------------------------------------------+
+ | Newton-CG | ``newton`` |
+ +-----------------------+------------------------------------------------------------------+
+ | COBYLA | ``cobyla`` |
+ +-----------------------+------------------------------------------------------------------+
+ | Truncated Newton | ``tnc`` |
+ +-----------------------+------------------------------------------------------------------+
+ | Dogleg | ``dogleg`` |
+ +-----------------------+------------------------------------------------------------------+
+ | Sequential Linear | ``slsqp`` |
+ | Squares Programming | |
+ +-----------------------+------------------------------------------------------------------+
+ | Differential | ``differential_evolution`` |
+ | Evolution | |
+ +-----------------------+------------------------------------------------------------------+
+
+
+.. note::
+
+ The objective function for the Levenberg-Marquardt method **must**
+ return an array, with more elements than variables. All other methods
+ can return either a scalar value or an array.
+
+
+.. warning::
+
+ Much of this documentation assumes that the Levenberg-Marquardt method is
+ the method used. Many of the fit statistics and estimates for
+ uncertainties in parameters discussed in :ref:`fit-results-label` are
+ done only for this method.
+
+.. _fit-results-label:
+
+:class:`MinimizerResult` -- the optimization result
+========================================================
+
+
+
+.. class:: MinimizerResult(**kws)
+
+.. versionadded:: 0.9.0
+
+An optimization with :func:`minimize` or :meth:`Minimizer.minimize`
+will return a :class:`MinimizerResult` object. This is an otherwise
+plain container object (that is, with no methods of its own) that
+simply holds the results of the minimization. These results will
+include several pieces of informational data such as status and error
+messages, fit statistics, and the updated parameters themselves.
+
+Importantly, the parameters passed in to :meth:`Minimizer.minimize`
+will be not be changed. To to find the best-fit values, uncertainties
+and so on for each parameter, one must use the
+:attr:`MinimizerResult.params` attribute.
+
+.. attribute:: params
+
+ the :class:`Parameters` actually used in the fit, with updated
+ values, :attr:`stderr` and :attr:`correl`.
+
+.. attribute:: var_names
+
+ ordered list of variable parameter names used in optimization, and
+ useful for understanding the the values in :attr:`init_vals` and
+ :attr:`covar`.
+
+.. attribute:: covar
+
+ covariance matrix from minimization (`leastsq` only), with
+ rows/columns using :attr:`var_names`.
+
+.. attribute:: init_vals
+
+ list of initial values for variable parameters using :attr:`var_names`.
+
+.. attribute:: nfev
+
+ number of function evaluations
+
+.. attribute:: success
+
+ boolean (``True``/``False``) for whether fit succeeded.
+
+.. attribute:: errorbars
+
+ boolean (``True``/``False``) for whether uncertainties were
+ estimated.
+
+.. attribute:: message
+
+ message about fit success.
+
+.. attribute:: ier
+
+ integer error value from :scipydoc:`optimize.leastsq` (`leastsq` only).
+
+.. attribute:: lmdif_message
+
+ message from :scipydoc:`optimize.leastsq` (`leastsq` only).
+
+.. attribute:: nvarys
+
+ number of variables in fit :math:`N_{\rm varys}`
+
+.. attribute:: ndata
+
+ number of data points: :math:`N`
+
+.. attribute:: nfree `
+
+ degrees of freedom in fit: :math:`N - N_{\rm varys}`
+
+.. attribute:: residual
+
+ residual array, return value of :func:`func`: :math:`{\rm Resid}`
+
+.. attribute:: chisqr
+
+ chi-square: :math:`\chi^2 = \sum_i^N [{\rm Resid}_i]^2`
+
+.. attribute:: redchi
+
+ reduced chi-square: :math:`\chi^2_{\nu}= {\chi^2} / {(N - N_{\rm
+ varys})}`
+
+.. attribute:: aic
+
+ Akaike Information Criterion statistic (see below)
+
+.. attribute:: bic
+
+ Bayesian Information Criterion statistic (see below).
+
+
+
+Goodness-of-Fit Statistics
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. _goodfit-table:
+
+ Table of Fit Results: These values, including the standard Goodness-of-Fit statistics,
+ are all attributes of the :class:`MinimizerResult` object returned by
+ :func:`minimize` or :meth:`Minimizer.minimize`.
+
++----------------------+----------------------------------------------------------------------------+
+| Attribute Name | Description / Formula |
++======================+============================================================================+
+| nfev | number of function evaluations |
++----------------------+----------------------------------------------------------------------------+
+| nvarys | number of variables in fit :math:`N_{\rm varys}` |
++----------------------+----------------------------------------------------------------------------+
+| ndata | number of data points: :math:`N` |
++----------------------+----------------------------------------------------------------------------+
+| nfree ` | degrees of freedom in fit: :math:`N - N_{\rm varys}` |
++----------------------+----------------------------------------------------------------------------+
+| residual | residual array, return value of :func:`func`: :math:`{\rm Resid}` |
++----------------------+----------------------------------------------------------------------------+
+| chisqr | chi-square: :math:`\chi^2 = \sum_i^N [{\rm Resid}_i]^2` |
++----------------------+----------------------------------------------------------------------------+
+| redchi | reduced chi-square: :math:`\chi^2_{\nu}= {\chi^2} / {(N - N_{\rm varys})}` |
++----------------------+----------------------------------------------------------------------------+
+| aic | Akaike Information Criterion statistic (see below) |
++----------------------+----------------------------------------------------------------------------+
+| bic | Bayesian Information Criterion statistic (see below) |
++----------------------+----------------------------------------------------------------------------+
+| var_names | ordered list of variable parameter names used for init_vals and covar |
++----------------------+----------------------------------------------------------------------------+
+| covar | covariance matrix (with rows/columns using var_names |
++----------------------+----------------------------------------------------------------------------+
+| init_vals | list of initial values for variable parameters |
++----------------------+----------------------------------------------------------------------------+
+
+Note that the calculation of chi-square and reduced chi-square assume
+that the returned residual function is scaled properly to the
+uncertainties in the data. For these statistics to be meaningful, the
+person writing the function to be minimized must scale them properly.
+
+After a fit using using the :meth:`leastsq` method has completed
+successfully, standard errors for the fitted variables and correlations
+between pairs of fitted variables are automatically calculated from the
+covariance matrix. The standard error (estimated :math:`1\sigma`
+error-bar) go into the :attr:`stderr` attribute of the Parameter. The
+correlations with all other variables will be put into the
+:attr:`correl` attribute of the Parameter -- a dictionary with keys for
+all other Parameters and values of the corresponding correlation.
+
+In some cases, it may not be possible to estimate the errors and
+correlations. For example, if a variable actually has no practical effect
+on the fit, it will likely cause the covariance matrix to be singular,
+making standard errors impossible to estimate. Placing bounds on varied
+Parameters makes it more likely that errors cannot be estimated, as being
+near the maximum or minimum value makes the covariance matrix singular. In
+these cases, the :attr:`errorbars` attribute of the fit result
+(:class:`Minimizer` object) will be ``False``.
+
+
+.. _information_criteria_label:
+
+Akaike and Bayesian Information Criteria
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The :class:`MinimizerResult` includes the traditional chi-square and reduced chi-square statistics:
+
+.. math::
+ :nowrap:
+
+ \begin{eqnarray*}
+ \chi^2 &=& \sum_i^N r_i^2 \\
+ \chi^2_\nu &=& = \chi^2 / (N-N_{\rm varys})
+ \end{eqnarray*}
+
+where :math:`r` is the residual array returned by the objective function
+(likely to be ``(data-model)/uncertainty`` for data modeling usages),
+:math:`N` is the number of data points (``ndata``), and :math:`N_{\rm
+varys}` is number of variable parameters.
+
+Also included are the `Akaike Information Criterion
+<http://en.wikipedia.org/wiki/Akaike_information_criterion>`_, and
+`Bayesian Information Criterion
+<http://en.wikipedia.org/wiki/Bayesian_information_criterion>`_ statistics,
+held in the ``aic`` and ``bic`` attributes, respectively. These give slightly
+different measures of the relative quality for a fit, trying to balance
+quality of fit with the number of variable parameters used in the fit.
+These are calculated as
+
+.. math::
+ :nowrap:
+
+ \begin{eqnarray*}
+ {\rm aic} &=& N \ln(\chi^2/N) + 2 N_{\rm varys} \\
+ {\rm bic} &=& N \ln(\chi^2/N) + \ln(N) *N_{\rm varys} \\
+ \end{eqnarray*}
+
+
+When comparing fits with different numbers of varying parameters, one
+typically selects the model with lowest reduced chi-square, Akaike
+information criterion, and/or Bayesian information criterion. Generally,
+the Bayesian information criterion is considered the most conservative of
+these statistics.
+
+.. _fit-itercb-label:
+
+
+Using a Iteration Callback Function
+====================================
+
+An iteration callback function is a function to be called at each
+iteration, just after the objective function is called. The iteration
+callback allows user-supplied code to be run at each iteration, and can be
+used to abort a fit.
+
+.. function:: iter_cb(params, iter, resid, *args, **kws):
+
+ user-supplied function to be run at each iteration
+
+ :param params: parameters.
+ :type params: :class:`Parameters`.
+ :param iter: iteration number
+ :type iter: integer
+ :param resid: residual array.
+ :type resid: ndarray
+ :param args: positional arguments. Must match ``args`` argument to :func:`minimize`
+ :param kws: keyword arguments. Must match ``kws`` argument to :func:`minimize`
+ :return: residual array (generally data-model) to be minimized in the least-squares sense.
+ :rtype: ``None`` for normal behavior, any value like ``True`` to abort fit.
+
+
+Normally, the iteration callback would have no return value or return
+``None``. To abort a fit, have this function return a value that is
+``True`` (including any non-zero integer). The fit will also abort if any
+exception is raised in the iteration callback. When a fit is aborted this
+way, the parameters will have the values from the last iteration. The fit
+statistics are not likely to be meaningful, and uncertainties will not be computed.
+
+
+.. module:: Minimizer
+
+.. _fit-minimizer-label:
+
+Using the :class:`Minimizer` class
+=======================================
+
+For full control of the fitting process, you'll want to create a
+:class:`Minimizer` object.
+
+.. class:: Minimizer(function, params, fcn_args=None, fcn_kws=None, iter_cb=None, scale_covar=True, **kws)
+
+ creates a Minimizer, for more detailed access to fitting methods and attributes.
+
+ :param function: objective function to return fit residual. See :ref:`fit-func-label` for details.
+ :type function: callable.
+ :param params: a dictionary of Parameters. Keywords must be strings
+ that match ``[a-z_][a-z0-9_]*`` and is not a python
+ reserved word. Each value must be :class:`Parameter`.
+ :type params: dict
+ :param fcn_args: arguments tuple to pass to the residual function as positional arguments.
+ :type fcn_args: tuple
+ :param fcn_kws: dictionary to pass to the residual function as keyword arguments.
+ :type fcn_kws: dict
+ :param iter_cb: function to be called at each fit iteration. See :ref:`fit-itercb-label` for details.
+ :type iter_cb: callable or ``None``
+ :param scale_covar: flag for automatically scaling covariance matrix and uncertainties to reduced chi-square (``leastsq`` only)
+ :type scale_covar: bool (default ``True``).
+ :param kws: dictionary to pass as keywords to the underlying :mod:`scipy.optimize` method.
+ :type kws: dict
+
+The Minimizer object has a few public methods:
+
+.. method:: minimize(method='leastsq', params=None, **kws)
+
+ perform fit using either :meth:`leastsq` or :meth:`scalar_minimize`.
+
+ :param method: name of fitting method. Must be one of the names in
+ :ref:`Table of Supported Fitting Methods <fit-methods-table>`
+ :type method: str.
+ :param params: a :class:`Parameters` dictionary for starting values
+ :type params: :class:`Parameters` or `None`
+
+ :return: :class:`MinimizerResult` object, containing updated
+ parameters, fitting statistics, and information.
+
+.. versionchanged:: 0.9.0
+ return value changed to :class:`MinimizerResult`
+
+ Additional keywords are passed on to the correspond :meth:`leastsq`
+ or :meth:`scalar_minimize` method.
+
+
+.. method:: leastsq(params=None, scale_covar=True, **kws)
+
+ perform fit with Levenberg-Marquardt algorithm. Keywords will be
+ passed directly to :scipydoc:`optimize.leastsq`. By default,
+ numerical derivatives are used, and the following arguments are set:
+
+
+ +------------------+----------------+------------------------------------------------------------+
+ | :meth:`leastsq` | Default Value | Description |
+ | arg | | |
+ +==================+================+============================================================+
+ | xtol | 1.e-7 | Relative error in the approximate solution |
+ +------------------+----------------+------------------------------------------------------------+
+ | ftol | 1.e-7 | Relative error in the desired sum of squares |
+ +------------------+----------------+------------------------------------------------------------+
+ | maxfev | 2000*(nvar+1) | maximum number of function calls (nvar= # of variables) |
+ +------------------+----------------+------------------------------------------------------------+
+ | Dfun | ``None`` | function to call for Jacobian calculation |
+ +------------------+----------------+------------------------------------------------------------+
+
+
+.. versionchanged:: 0.9.0
+ return value changed to :class:`MinimizerResult`
+
+.. method:: scalar_minimize(method='Nelder-Mead', params=None, hess=None, tol=None, **kws)
+
+ perform fit with any of the scalar minimization algorithms supported by
+ :scipydoc:`optimize.minimize`.
+
+ +-------------------------+-----------------+-----------------------------------------------------+
+ | :meth:`scalar_minimize` | Default Value | Description |
+ | arg | | |
+ +=========================+=================+=====================================================+
+ | method | ``Nelder-Mead`` | fitting method |
+ +-------------------------+-----------------+-----------------------------------------------------+
+ | tol | 1.e-7 | fitting and parameter tolerance |
+ +-------------------------+-----------------+-----------------------------------------------------+
+ | hess | None | Hessian of objective function |
+ +-------------------------+-----------------+-----------------------------------------------------+
+
+.. versionchanged:: 0.9.0
+ return value changed to :class:`MinimizerResult`
+
+.. method:: prepare_fit(**kws)
+
+ prepares and initializes model and Parameters for subsequent
+ fitting. This routine prepares the conversion of :class:`Parameters`
+ into fit variables, organizes parameter bounds, and parses, "compiles"
+ and checks constrain expressions. The method also creates and returns
+ a new instance of a :class:`MinimizerResult` object that contains the
+ copy of the Parameters that will actually be varied in the fit.
+
+ This method is called directly by the fitting methods, and it is
+ generally not necessary to call this function explicitly.
+
+.. versionchanged:: 0.9.0
+ return value changed to :class:`MinimizerResult`
+
+
+
+.. method:: emcee(params=None, steps=1000, nwalkers=100, burn=0, thin=1, ntemps=1, pos=None, reuse_sampler=False, workers=1, float_behavior='posterior', is_weighted=True, seed=None)
+
+ Bayesian sampling of the posterior distribution for the parameters using the `emcee`
+ Markov Chain Monte Carlo package. The method assumes that the prior is Uniform. You need
+ to have `emcee` installed to use this method.
+
+ :param params: a :class:`Parameters` dictionary for starting values
+ :type params: :class:`Parameters` or `None`
+ :param steps: How many samples you would like to draw from the posterior
+ distribution for each of the walkers?
+ :type steps: int
+ :param nwalkers: Should be set so :math:`nwalkers >> nvarys`, where `nvarys`
+ are the number of parameters being varied during the fit.
+ "Walkers are the members of the ensemble. They are almost
+ like separate Metropolis-Hastings chains but, of course,
+ the proposal distribution for a given walker depends on the
+ positions of all the other walkers in the ensemble." - from
+ [1]_.
+ :type nwalkers: int
+ :param burn: Discard this many samples from the start of the sampling regime.
+ :type burn: int
+ :param thin: Only accept 1 in every `thin` samples.
+ :type thin: int
+ :param ntemps: If `ntemps > 1` perform a Parallel Tempering.
+ :type ntemps: int
+ :param pos: Specify the initial positions for the sampler. If `ntemps == 1`
+ then `pos.shape` should be `(nwalkers, nvarys)`. Otherwise,
+ `(ntemps, nwalkers, nvarys)`. You can also initialise using a
+ previous chain that had the same `ntemps`, `nwalkers` and `nvarys`.
+ :type pos: np.ndarray
+ :param reuse_sampler: If you have already run :meth:`emcee` on a given
+ :class:`Minimizer` object then it possesses an internal sampler
+ attribute. You can continue to draw from the same sampler (retaining
+ the chain history) if you set this option to `True`. Otherwise a new
+ sampler is created. The `nwalkers`, `ntemps` and `params` keywords
+ are ignored with this option.
+ **Important**: the :class:`Parameters` used to create the sampler
+ must not change in-between calls to :meth:`emcee`. Alteration of
+ :class:`Parameters` would include changed ``min``, ``max``,
+ ``vary`` and ``expr`` attributes. This may happen, for example, if
+ you use an altered :class:`Parameters` object and call the
+ :meth:`minimize` method in-between calls to :meth:`emcee` .
+ :type reuse_sampler: bool
+ :param workers: For parallelization of sampling. It can be any Pool-like object
+ with a map method that follows the same calling sequence as the
+ built-in map function. If int is given as the argument, then a
+ multiprocessing-based pool is spawned internally with the
+ corresponding number of parallel processes. 'mpi4py'-based
+ parallelization and 'joblib'-based parallelization pools can also
+ be used here. **Note**: because of multiprocessing overhead it may
+ only be worth parallelising if the objective function is expensive
+ to calculate, or if there are a large number of objective
+ evaluations per step (`ntemps * nwalkers * nvarys`).
+ :type workers: int or Pool-like
+ :type float_behavior: str
+ :param float_behavior: Specifies the meaning of the objective function if it
+ returns a float. One of:
+
+ 'posterior' - the objective function returns a log-posterior probability
+
+ 'chi2' - the objective function is returning :math:`\chi^2`.
+
+ See Notes for further details.
+ :param is_weighted: Has your objective function been weighted by measurement
+ uncertainties? If `is_weighted is True` then your objective
+ function is assumed to return residuals that have been divided by
+ the true measurement uncertainty `(data - model) / sigma`. If
+ `is_weighted is False` then the objective function is assumed to
+ return unweighted residuals, `data - model`. In this case `emcee`
+ will employ a positive measurement uncertainty during the sampling.
+ This measurement uncertainty will be present in the output params
+ and output chain with the name `__lnsigma`. A side effect of this
+ is that you cannot use this parameter name yourself.
+ **Important** this parameter only has any effect if your objective
+ function returns an array. If your objective function returns a
+ float, then this parameter is ignored. See Notes for more details.
+ :type is_weighted: bool
+ :param seed: If `seed` is an int, a new `np.random.RandomState` instance is used,
+ seeded with `seed`.
+ If `seed` is already a `np.random.RandomState` instance, then that
+ `np.random.RandomState` instance is used.
+ Specify `seed` for repeatable sampling.
+ :type seed: int or np.random.RandomState
+
+ :return: :class:`MinimizerResult` object containing updated params, statistics,
+ etc. The :class:`MinimizerResult` also contains the ``chain``,
+ ``flatchain`` and ``lnprob`` attributes. The ``chain``
+ and ``flatchain`` attributes contain the samples and have the shape
+ `(nwalkers, (steps - burn) // thin, nvarys)` or
+ `(ntemps, nwalkers, (steps - burn) // thin, nvarys)`,
+ depending on whether Parallel tempering was used or not.
+ `nvarys` is the number of parameters that are allowed to vary.
+ The ``flatchain`` attribute is a :class:`pandas.DataFrame` of the
+ flattened chain, `chain.reshape(-1, nvarys)`. To access flattened
+ chain values for a particular parameter use
+ `result.flatchain[parname]`. The ``lnprob`` attribute contains the
+ log probability for each sample in ``chain``. The sample with the
+ highest probability corresponds to the maximum likelihood estimate.
+
+ This method samples the posterior distribution of the parameters using
+ Markov Chain Monte Carlo. To do so it needs to calculate the
+ log-posterior probability of the model parameters, `F`, given the data,
+ `D`, :math:`\ln p(F_{true} | D)`. This 'posterior probability' is
+ calculated as:
+
+ .. math::
+
+ \ln p(F_{true} | D) \propto \ln p(D | F_{true}) + \ln p(F_{true})
+
+ where :math:`\ln p(D | F_{true})` is the 'log-likelihood' and
+ :math:`\ln p(F_{true})` is the 'log-prior'. The default log-prior
+ encodes prior information already known about the model. This method
+ assumes that the log-prior probability is `-np.inf` (impossible) if the
+ one of the parameters is outside its limits. The log-prior probability
+ term is zero if all the parameters are inside their bounds (known as a
+ uniform prior). The log-likelihood function is given by [1]_:
+
+ .. math::
+
+ \ln p(D|F_{true}) = -\frac{1}{2}\sum_n \left[\frac{\left(g_n(F_{true}) - D_n \right)^2}{s_n^2}+\ln (2\pi s_n^2)\right]
+
+ The first summand in the square brackets represents the residual for a
+ given datapoint (:math:`g` being the generative model) . This term
+ represents :math:`\chi^2` when summed over all datapoints.
+ Ideally the objective function used to create :class:`lmfit.Minimizer` should
+ return the log-posterior probability, :math:`\ln p(F_{true} | D)`.
+ However, since the in-built log-prior term is zero, the objective
+ function can also just return the log-likelihood, unless you wish to
+ create a non-uniform prior.
+
+ If a float value is returned by the objective function then this value
+ is assumed by default to be the log-posterior probability, i.e.
+ `float_behavior is 'posterior'`. If your objective function returns
+ :math:`\chi^2`, then you should use a value of `'chi2'` for
+ `float_behavior`. `emcee` will then multiply your :math:`\chi^2` value
+ by -0.5 to obtain the posterior probability.
+
+ However, the default behaviour of many objective functions is to return
+ a vector of (possibly weighted) residuals. Therefore, if your objective
+ function returns a vector, `res`, then the vector is assumed to contain
+ the residuals. If `is_weighted is True` then your residuals are assumed
+ to be correctly weighted by the standard deviation of the data points
+ (`res = (data - model) / sigma`) and the log-likelihood (and
+ log-posterior probability) is calculated as: `-0.5 * np.sum(res **2)`.
+ This ignores the second summand in the square brackets. Consequently, in
+ order to calculate a fully correct log-posterior probability value your
+ objective function should return a single value. If `is_weighted is False`
+ then the data uncertainty, :math:`s_n`, will be treated as a nuisance
+ parameter and will be marginalised out. This is achieved by employing a
+ strictly positive uncertainty (homoscedasticity) for each data point,
+ :math:`s_n=exp(\_\_lnsigma)`. `__lnsigma` will be present in
+ `MinimizerResult.params`, as well as `Minimizer.chain`, `nvarys` will also be
+ increased by one.
+
+ .. [1] http://dan.iel.fm/emcee/current/user/line/
+
+
+.. _label-emcee:
+
+:meth:`emcee` - calculating the posterior probability distribution of parameters
+==============================================================================================
+
+:meth:`emcee` can be used to obtain the posterior probability distribution of
+parameters, given a set of experimental data. An example problem is a double
+exponential decay. A small amount of Gaussian noise is also added in::
+
+ >>> import numpy as np
+ >>> import lmfit
+ >>> import matplotlib.pyplot as plt
+ >>> x = np.linspace(1, 10, 250)
+ >>> np.random.seed(0)
+ >>> y = 3.0 * np.exp(-x / 2) - 5.0 * np.exp(-(x - 0.1) / 10.) + 0.1 * np.random.randn(len(x))
+ >>> plt.plot(x, y)
+ >>> plt.show()
+
+.. image:: _images/emcee_dbl_exp.png
+
+Create a Parameter set for the initial guesses::
+
+ >>> p = lmfit.Parameters()
+ >>> p.add_many(('a1', 4.), ('a2', 4.), ('t1', 3.), ('t2', 3., True))
+
+ >>> def residual(p):
+ ... v = p.valuesdict()
+ ... return v['a1'] * np.exp(-x / v['t1']) + v['a2'] * np.exp(-(x - 0.1) / v['t2']) - y
+
+Solving with :func:`minimize` gives the Maximum Likelihood solution.::
+
+ >>> mi = lmfit.minimize(residual, p, method='Nelder')
+ >>> lmfit.printfuncs.report_fit(mi.params, min_correl=0.5)
+ [[Variables]]
+ a1: 2.98623688 (init= 4)
+ a2: -4.33525596 (init= 4)
+ t1: 1.30993185 (init= 3)
+ t2: 11.8240752 (init= 3)
+ [[Correlations]] (unreported correlations are < 0.500)
+ >>> plt.plot(x, y)
+ >>> plt.plot(x, residual(mi.params) + y, 'r')
+ >>> plt.show()
+
+.. image:: _images/emcee_dbl_exp2.png
+
+However, this doesn't give a probability distribution for the parameters.
+Furthermore, we wish to deal with the data uncertainty. This is called
+marginalisation of a nuisance parameter. emcee requires a function that returns
+the log-posterior probability. The log-posterior probability is a sum of the
+log-prior probability and log-likelihood functions. The log-prior probability is
+assumed to be zero if all the parameters are within their bounds and `-np.inf`
+if any of the parameters are outside their bounds.::
+
+ >>> # add a noise parameter
+ >>> mi.params.add('f', value=1, min=0.001, max=2)
+
+ >>> # This is the log-likelihood probability for the sampling. We're going to estimate the
+ >>> # size of the uncertainties on the data as well.
+ >>> def lnprob(p):
+ ... resid = residual(p)
+ ... s = p['f']
+ ... resid *= 1 / s
+ ... resid *= resid
+ ... resid += np.log(2 * np.pi * s**2)
+ ... return -0.5 * np.sum(resid)
+
+Now we have to set up the minimizer and do the sampling.::
+
+ >>> mini = lmfit.Minimizer(lnprob, mi.params)
+ >>> res = mini.emcee(burn=300, steps=600, thin=10, params=mi.params)
+
+Lets have a look at those posterior distributions for the parameters. This requires
+installation of the `corner` package.::
+
+ >>> import corner
+ >>> corner.corner(res.flatchain, labels=res.var_names, truths=list(res.params.valuesdict().values()))
+
+.. image:: _images/emcee_triangle.png
+
+The values reported in the :class:`MinimizerResult` are the medians of the
+probability distributions and a 1 sigma quantile, estimated as half the
+difference between the 15.8 and 84.2 percentiles. The median value is not
+necessarily the same as the Maximum Likelihood Estimate. We'll get that as well.
+You can see that we recovered the right uncertainty level on the data.::
+
+ >>> print("median of posterior probability distribution")
+ >>> print('------------------------------------------')
+ >>> lmfit.report_fit(res.params)
+ median of posterior probability distribution
+ ------------------------------------------
+ [[Variables]]
+ a1: 3.00975345 +/- 0.151034 (5.02%) (init= 2.986237)
+ a2: -4.35419204 +/- 0.127505 (2.93%) (init=-4.335256)
+ t1: 1.32726415 +/- 0.142995 (10.77%) (init= 1.309932)
+ t2: 11.7911935 +/- 0.495583 (4.20%) (init= 11.82408)
+ f: 0.09805494 +/- 0.004256 (4.34%) (init= 1)
+ [[Correlations]] (unreported correlations are < 0.100)
+ C(a2, t2) = 0.981
+ C(a2, t1) = -0.927
+ C(t1, t2) = -0.880
+ C(a1, t1) = -0.519
+ C(a1, a2) = 0.195
+ C(a1, t2) = 0.146
+
+ >>> # find the maximum likelihood solution
+ >>> highest_prob = np.argmax(res.lnprob)
+ >>> hp_loc = np.unravel_index(highest_prob, res.lnprob.shape)
+ >>> mle_soln = res.chain[hp_loc]
+ >>> for i, par in enumerate(p):
+ ... p[par].value = mle_soln[i]
+
+ >>> print("\nMaximum likelihood Estimation")
+ >>> print('-----------------------------')
+ >>> print(p)
+ Maximum likelihood Estimation
+ -----------------------------
+ Parameters([('a1', <Parameter 'a1', 2.9943337359308981, bounds=[-inf:inf]>),
+ ('a2', <Parameter 'a2', -4.3364489105166593, bounds=[-inf:inf]>),
+ ('t1', <Parameter 't1', 1.3124544105342462, bounds=[-inf:inf]>),
+ ('t2', <Parameter 't2', 11.80612160586597, bounds=[-inf:inf]>)])
+
+ >>> # Finally lets work out a 1 and 2-sigma error estimate for 't1'
+ >>> quantiles = np.percentile(res.flatchain['t1'], [2.28, 15.9, 50, 84.2, 97.7])
+ >>> print("2 sigma spread", 0.5 * (quantiles[-1] - quantiles[0]))
+ 2 sigma spread 0.298878202908
+
+Getting and Printing Fit Reports
+===========================================
+
+.. function:: fit_report(result, modelpars=None, show_correl=True, min_correl=0.1)
+
+ generate and return text of report of best-fit values, uncertainties,
+ and correlations from fit.
+
+ :param result: :class:`MinimizerResult` object as returned by :func:`minimize`.
+ :param modelpars: Parameters with "Known Values" (optional, default None)
+ :param show_correl: whether to show list of sorted correlations [``True``]
+ :param min_correl: smallest correlation absolute value to show [0.1]
+
+ If the first argument is a :class:`Parameters` object,
+ goodness-of-fit statistics will not be included.
+
+.. function:: report_fit(result, modelpars=None, show_correl=True, min_correl=0.1)
+
+ print text of report from :func:`fit_report`.
+
+An example fit with report would be
+
+.. literalinclude:: ../examples/doc_withreport.py
+
+which would write out::
+
+ [[Fit Statistics]]
+ # function evals = 85
+ # data points = 1001
+ # variables = 4
+ chi-square = 498.812
+ reduced chi-square = 0.500
+ Akaike info crit = -685.215
+ Bayesian info crit = -665.579
+ [[Variables]]
+ amp: 13.9121944 +/- 0.141202 (1.01%) (init= 13)
+ period: 5.48507044 +/- 0.026664 (0.49%) (init= 2)
+ shift: 0.16203676 +/- 0.014056 (8.67%) (init= 0)
+ decay: 0.03264538 +/- 0.000380 (1.16%) (init= 0.02)
+ [[Correlations]] (unreported correlations are < 0.100)
+ C(period, shift) = 0.797
+ C(amp, decay) = 0.582
+ C(amp, shift) = -0.297
+ C(amp, period) = -0.243
+ C(shift, decay) = -0.182
+ C(period, decay) = -0.150
diff --git a/doc/index.rst b/doc/index.rst
index 8430f2b..5a2205a 100644
--- a/doc/index.rst
+++ b/doc/index.rst
@@ -1,68 +1,68 @@
-.. lmfit documentation master file,
-
-Non-Linear Least-Square Minimization and Curve-Fitting for Python
-===========================================================================
-
-.. _Levenberg-Marquardt: http://en.wikipedia.org/wiki/Levenberg-Marquardt_algorithm
-.. _MINPACK-1: http://en.wikipedia.org/wiki/MINPACK
-
-
-.. warning::
-
- Upgrading scripts from version 0.8.3 to 0.9.0? See :ref:`whatsnew_090_label`
-
-
-Lmfit provides a high-level interface to non-linear optimization and curve
-fitting problems for Python. Lmfit builds on and extends many of the
-optimizatin algorithm of :mod:`scipy.optimize`, especially the
-`Levenberg-Marquardt`_ method from :func:`scipy.optimize.leastsq`.
-
-Lmfit provides a number of useful enhancements to optimization and data
-fitting problems, including:
-
- * Using :class:`Parameter` objects instead of plain floats as variables.
- A :class:`Parameter` has a value that can be varied in the fit, have a
- fixed value, or have upper and/or lower bounds. A Parameter can even
- have a value that is constrained by an algebraic expression of other
- Parameter values.
-
- * Ease of changing fitting algorithms. Once a fitting model is set up,
- one can change the fitting algorithm used to find the optimal solution
- without changing the objective function.
-
- * Improved estimation of confidence intervals. While
- :func:`scipy.optimize.leastsq` will automatically calculate
- uncertainties and correlations from the covariance matrix, the accuracy
- of these estimates are often questionable. To help address this, lmfit
- has functions to explicitly explore parameter space to determine
- confidence levels even for the most difficult cases.
-
- * Improved curve-fitting with the :class:`Model` class. This
- extends the capabilities of :func:`scipy.optimize.curve_fit`, allowing
- you to turn a function that models for your data into a python class
- that helps you parametrize and fit data with that model.
-
- * Many :ref:`pre-built models <builtin_models_chapter>` for common
- lineshapes are included and ready to use.
-
-.. _lmfit github repository: http://github.com/lmfit/lmfit-py
-
-The lmfit package is Free software, using an MIT license. The software and
-this document are works in progress. If you are interested in
-participating in this effort please use the `lmfit github repository`_.
-
-
-.. toctree::
- :maxdepth: 2
-
- intro
- installation
- support
- faq
- parameters
- fitting
- model
- builtin_models
- confidence
- bounds
- constraints
+.. lmfit documentation master file,
+
+Non-Linear Least-Square Minimization and Curve-Fitting for Python
+===========================================================================
+
+.. _Levenberg-Marquardt: http://en.wikipedia.org/wiki/Levenberg-Marquardt_algorithm
+.. _MINPACK-1: http://en.wikipedia.org/wiki/MINPACK
+
+
+.. warning::
+
+ Upgrading scripts from version 0.8.3 to 0.9.0? See :ref:`whatsnew_090_label`
+
+
+Lmfit provides a high-level interface to non-linear optimization and curve
+fitting problems for Python. Lmfit builds on and extends many of the
+optimization algorithm of :mod:`scipy.optimize`, especially the
+`Levenberg-Marquardt`_ method from :scipydoc:`optimize.leastsq`.
+
+Lmfit provides a number of useful enhancements to optimization and data
+fitting problems, including:
+
+ * Using :class:`Parameter` objects instead of plain floats as variables.
+ A :class:`Parameter` has a value that can be varied in the fit, have a
+ fixed value, or have upper and/or lower bounds. A Parameter can even
+ have a value that is constrained by an algebraic expression of other
+ Parameter values.
+
+ * Ease of changing fitting algorithms. Once a fitting model is set up,
+ one can change the fitting algorithm used to find the optimal solution
+ without changing the objective function.
+
+ * Improved estimation of confidence intervals. While
+ :scipydoc:`optimize.leastsq` will automatically calculate
+ uncertainties and correlations from the covariance matrix, the accuracy
+ of these estimates are often questionable. To help address this, lmfit
+ has functions to explicitly explore parameter space to determine
+ confidence levels even for the most difficult cases.
+
+ * Improved curve-fitting with the :class:`Model` class. This
+ extends the capabilities of :scipydoc:`optimize.curve_fit`, allowing
+ you to turn a function that models for your data into a python class
+ that helps you parametrize and fit data with that model.
+
+ * Many :ref:`pre-built models <builtin_models_chapter>` for common
+ lineshapes are included and ready to use.
+
+.. _lmfit github repository: http://github.com/lmfit/lmfit-py
+
+The lmfit package is Free software, using an MIT license. The software and
+this document are works in progress. If you are interested in
+participating in this effort please use the `lmfit github repository`_.
+
+
+.. toctree::
+ :maxdepth: 2
+
+ intro
+ installation
+ support
+ faq
+ parameters
+ fitting
+ model
+ builtin_models
+ confidence
+ bounds
+ constraints
diff --git a/doc/installation.rst b/doc/installation.rst
index 9112fc6..f9adadd 100644
--- a/doc/installation.rst
+++ b/doc/installation.rst
@@ -1,82 +1,82 @@
-====================================
-Downloading and Installation
-====================================
-
-.. _lmfit github repository: http://github.com/lmfit/lmfit-py
-.. _Python Setup Tools: http://pypi.python.org/pypi/setuptools
-.. _pip: https://pip.pypa.io/
-.. _nose: http://nose.readthedocs.org/
-
-Prerequisites
-~~~~~~~~~~~~~~~
-
-The lmfit package requires Python, Numpy, and Scipy. Scipy version 0.13 or
-higher is recommended, but extensive testing on compatibility with various
-versions of scipy has not been done. Lmfit works with Python 2.7, 3.3 and
-3.4. No testing has been done with Python 3.5, but as the package is pure
-Python, relying only on scipy and numpy, no significant troubles are
-expected. The `nose`_ framework is required for running the test suite,
-and IPython and matplotib are recommended. If Pandas is available, it will
-be used in portions of lmfit.
-
-
-Downloads
-~~~~~~~~~~~~~
-
-
-The latest stable version of lmfit is available from `PyPi <http://pypi.python.org/pypi/lmfit/>`_.
-
-Installation
-~~~~~~~~~~~~~~~~~
-
-If you have `pip`_ installed, you can install lmfit with::
-
- pip install lmfit
-
-or, if you have `Python Setup Tools`_ installed, you install lmfit with::
-
- easy_install -U lmfit
-
-
-or, you can download the source kit, unpack it and install with::
-
- python setup.py install
-
-
-Development Version
-~~~~~~~~~~~~~~~~~~~~~~~~
-
-To get the latest development version, use::
-
- git clone http://github.com/lmfit/lmfit-py.git
-
-
-and install using::
-
- python setup.py install
-
-
-Testing
-~~~~~~~~~~
-
-A battery of tests scripts that can be run with the `nose`_ testing
-framework is distributed with lmfit in the ``tests`` folder. These are
-routinely run on the development version. Running ``nosetests`` should run
-all of these tests to completion without errors or failures.
-
-Many of the examples in this documentation are distributed with lmfit in
-the ``examples`` folder, and should also run for you. Many of these require
-
-
-Acknowledgements
-~~~~~~~~~~~~~~~~~~
-
-.. literalinclude:: ../THANKS.txt
-
-
-License
-~~~~~~~~~~~~~
-
-The LMFIT-py code is distribution under the following license:
-
-.. literalinclude:: ../LICENSE
+====================================
+Downloading and Installation
+====================================
+
+.. _lmfit github repository: http://github.com/lmfit/lmfit-py
+.. _Python Setup Tools: http://pypi.python.org/pypi/setuptools
+.. _pip: https://pip.pypa.io/
+.. _nose: http://nose.readthedocs.org/
+
+Prerequisites
+~~~~~~~~~~~~~~~
+
+The lmfit package requires Python, Numpy, and Scipy. Scipy version 0.13 or
+higher is recommended, but extensive testing on compatibility with various
+versions of scipy has not been done. Lmfit works with Python 2.7, 3.3 and
+3.4. No testing has been done with Python 3.5, but as the package is pure
+Python, relying only on scipy and numpy, no significant troubles are
+expected. The `nose`_ framework is required for running the test suite,
+and IPython and matplotib are recommended. If Pandas is available, it will
+be used in portions of lmfit.
+
+
+Downloads
+~~~~~~~~~~~~~
+
+
+The latest stable version of lmfit is available from `PyPi <http://pypi.python.org/pypi/lmfit/>`_.
+
+Installation
+~~~~~~~~~~~~~~~~~
+
+If you have `pip`_ installed, you can install lmfit with::
+
+ pip install lmfit
+
+or, if you have `Python Setup Tools`_ installed, you install lmfit with::
+
+ easy_install -U lmfit
+
+
+or, you can download the source kit, unpack it and install with::
+
+ python setup.py install
+
+
+Development Version
+~~~~~~~~~~~~~~~~~~~~~~~~
+
+To get the latest development version, use::
+
+ git clone http://github.com/lmfit/lmfit-py.git
+
+
+and install using::
+
+ python setup.py install
+
+
+Testing
+~~~~~~~~~~
+
+A battery of tests scripts that can be run with the `nose`_ testing
+framework is distributed with lmfit in the ``tests`` folder. These are
+routinely run on the development version. Running ``nosetests`` should run
+all of these tests to completion without errors or failures.
+
+Many of the examples in this documentation are distributed with lmfit in
+the ``examples`` folder, and should also run for you. Many of these require
+
+
+Acknowledgements
+~~~~~~~~~~~~~~~~~~
+
+.. literalinclude:: ../THANKS.txt
+
+
+License
+~~~~~~~~~~~~~
+
+The LMFIT-py code is distribution under the following license:
+
+.. literalinclude:: ../LICENSE
diff --git a/doc/intro.rst b/doc/intro.rst
index c480ae6..bc854f4 100644
--- a/doc/intro.rst
+++ b/doc/intro.rst
@@ -1,150 +1,150 @@
-.. _intro_chapter:
-
-===========================================================
-Getting started with Non-Linear Least-Squares Fitting
-===========================================================
-
-The lmfit package is designed to provide simple tools to help you build
-complex fitting models for non-linear least-squares problems and apply
-these models to real data. This section gives an overview of the concepts
-and describes how to set up and perform simple fits. Some basic knowledge
-of Python, numpy, and modeling data are assumed.
-
-To do a non-linear least-squares fit of a model to data or for a variety of other
-optimization problems, the main task is to write an *objective function*
-that takes the values of the fitting variables and calculates either a
-scalar value to be minimized or an array of values that is to be minimized
-in the least-squares sense. For many data fitting processes, the
-least-squares approach is used, and the objective function should
-return an array of (data-model), perhaps scaled by some weighting factor
-such as the inverse of the uncertainty in the data. For such a problem,
-the chi-square (:math:`\chi^2`) statistic is often defined as:
-
-.. math::
-
- \chi^2 = \sum_i^{N} \frac{[y^{\rm meas}_i - y_i^{\rm model}({\bf{v}})]^2}{\epsilon_i^2}
-
-where :math:`y_i^{\rm meas}` is the set of measured data, :math:`y_i^{\rm
-model}({\bf{v}})` is the model calculation, :math:`{\bf{v}}` is the set of
-variables in the model to be optimized in the fit, and :math:`\epsilon_i`
-is the estimated uncertainty in the data.
-
-In a traditional non-linear fit, one writes an objective function that takes the
-variable values and calculates the residual :math:`y^{\rm meas}_i -
-y_i^{\rm model}({\bf{v}})`, or the residual scaled by the data
-uncertainties, :math:`[y^{\rm meas}_i - y_i^{\rm
-model}({\bf{v}})]/{\epsilon_i}`, or some other weighting factor. As a
-simple example, one might write an objective function like this::
-
- def residual(vars, x, data, eps_data):
- amp = vars[0]
- phaseshift = vars[1]
- freq = vars[2]
- decay = vars[3]
-
- model = amp * sin(x * freq + phaseshift) * exp(-x*x*decay)
-
- return (data-model)/eps_data
-
-To perform the minimization with :mod:`scipy.optimize`, one would do::
-
- from scipy.optimize import leastsq
- vars = [10.0, 0.2, 3.0, 0.007]
- out = leastsq(residual, vars, args=(x, data, eps_data))
-
-Though it is wonderful to be able to use python for such optimization
-problems, and the scipy library is robust and easy to use, the approach
-here is not terribly different from how one would do the same fit in C or
-Fortran. There are several practical challenges to using this approach,
-including:
-
- a) The user has to keep track of the order of the variables, and their
- meaning -- vars[0] is the amplitude, vars[2] is the frequency, and so
- on, although there is no intrinsic meaning to this order.
-
- b) If the user wants to fix a particular variable (*not* vary it in the
- fit), the residual function has to be altered to have fewer variables,
- and have the corresponding constant value passed in some other way.
- While reasonable for simple cases, this quickly becomes a significant
- work for more complex models, and greatly complicates modeling for
- people not intimately familiar with the details of the fitting code.
-
- c) There is no simple, robust way to put bounds on values for the
- variables, or enforce mathematical relationships between the
- variables. In fact, those optimization methods that do provide
- bounds, require bounds to be set for all variables with separate
- arrays that are in the same arbitrary order as variable values.
- Again, this is acceptable for small or one-off cases, but becomes
- painful if the fitting model needs to change.
-
-These shortcomings are really do solely to the use of traditional arrays of
-variables, as matches closely the implementation of the Fortran code. The
-lmfit module overcomes these shortcomings by using objects -- a core reason for wokring with
-Python. The key concept for lmfit is to use :class:`Parameter`
-objects instead of plain floating point numbers as the variables for the
-fit. By using :class:`Parameter` objects (or the closely related
-:class:`Parameters` -- a dictionary of :class:`Parameter` objects), one can
-
- a) forget about the order of variables and refer to Parameters
- by meaningful names.
- b) place bounds on Parameters as attributes, without worrying about order.
- c) fix Parameters, without having to rewrite the objective function.
- d) place algebraic constraints on Parameters.
-
-To illustrate the value of this approach, we can rewrite the above example
-as::
-
- from lmfit import minimize, Parameters
-
- def residual(params, x, data, eps_data):
- amp = params['amp'].value
- pshift = params['phase'].value
- freq = params['frequency'].value
- decay = params['decay'].value
-
- model = amp * sin(x * freq + pshift) * exp(-x*x*decay)
-
- return (data-model)/eps_data
-
- params = Parameters()
- params.add('amp', value=10)
- params.add('decay', value=0.007)
- params.add('phase', value=0.2)
- params.add('frequency', value=3.0)
-
- out = minimize(residual, params, args=(x, data, eps_data))
-
-
-At first look, we simply replaced a list of values with a dictionary,
-accessed by name -- not a huge improvement. But each of the named
-:class:`Parameter` in the :class:`Parameters` object holds additional
-attributes to modify the value during the fit. For example, Parameters can
-be fixed or bounded. This can be done during definition::
-
- params = Parameters()
- params.add('amp', value=10, vary=False)
- params.add('decay', value=0.007, min=0.0)
- params.add('phase', value=0.2)
- params.add('frequency', value=3.0, max=10)
-
-where ``vary=False`` will prevent the value from changing in the fit, and
-``min=0.0`` will set a lower bound on that parameters value). It can also be done
-later by setting the corresponding attributes after they have been
-created::
-
- params['amp'].vary = False
- params['decay'].min = 0.10
-
-Importantly, our objective function remains unchanged.
-
-The `params` object can be copied and modified to make many user-level
-changes to the model and fitting process. Of course, most of the
-information about how your data is modeled goes into the objective
-function, but the approach here allows some external control; that is, control by
-the **user** performing the fit, instead of by the author of the
-objective function.
-
-Finally, in addition to the :class:`Parameters` approach to fitting data,
-lmfit allows switching optimization methods without changing
-the objective function, provides tools for writing fitting reports, and
-provides better determination of Parameters confidence levels.
+.. _intro_chapter:
+
+===========================================================
+Getting started with Non-Linear Least-Squares Fitting
+===========================================================
+
+The lmfit package is designed to provide simple tools to help you build
+complex fitting models for non-linear least-squares problems and apply
+these models to real data. This section gives an overview of the concepts
+and describes how to set up and perform simple fits. Some basic knowledge
+of Python, numpy, and modeling data are assumed.
+
+To do a non-linear least-squares fit of a model to data or for a variety of other
+optimization problems, the main task is to write an *objective function*
+that takes the values of the fitting variables and calculates either a
+scalar value to be minimized or an array of values that is to be minimized
+in the least-squares sense. For many data fitting processes, the
+least-squares approach is used, and the objective function should
+return an array of (data-model), perhaps scaled by some weighting factor
+such as the inverse of the uncertainty in the data. For such a problem,
+the chi-square (:math:`\chi^2`) statistic is often defined as:
+
+.. math::
+
+ \chi^2 = \sum_i^{N} \frac{[y^{\rm meas}_i - y_i^{\rm model}({\bf{v}})]^2}{\epsilon_i^2}
+
+where :math:`y_i^{\rm meas}` is the set of measured data, :math:`y_i^{\rm
+model}({\bf{v}})` is the model calculation, :math:`{\bf{v}}` is the set of
+variables in the model to be optimized in the fit, and :math:`\epsilon_i`
+is the estimated uncertainty in the data.
+
+In a traditional non-linear fit, one writes an objective function that takes the
+variable values and calculates the residual :math:`y^{\rm meas}_i -
+y_i^{\rm model}({\bf{v}})`, or the residual scaled by the data
+uncertainties, :math:`[y^{\rm meas}_i - y_i^{\rm
+model}({\bf{v}})]/{\epsilon_i}`, or some other weighting factor. As a
+simple example, one might write an objective function like this::
+
+ def residual(vars, x, data, eps_data):
+ amp = vars[0]
+ phaseshift = vars[1]
+ freq = vars[2]
+ decay = vars[3]
+
+ model = amp * sin(x * freq + phaseshift) * exp(-x*x*decay)
+
+ return (data-model)/eps_data
+
+To perform the minimization with :mod:`scipy.optimize`, one would do::
+
+ from scipy.optimize import leastsq
+ vars = [10.0, 0.2, 3.0, 0.007]
+ out = leastsq(residual, vars, args=(x, data, eps_data))
+
+Though it is wonderful to be able to use python for such optimization
+problems, and the scipy library is robust and easy to use, the approach
+here is not terribly different from how one would do the same fit in C or
+Fortran. There are several practical challenges to using this approach,
+including:
+
+ a) The user has to keep track of the order of the variables, and their
+ meaning -- vars[0] is the amplitude, vars[2] is the frequency, and so
+ on, although there is no intrinsic meaning to this order.
+
+ b) If the user wants to fix a particular variable (*not* vary it in the
+ fit), the residual function has to be altered to have fewer variables,
+ and have the corresponding constant value passed in some other way.
+ While reasonable for simple cases, this quickly becomes a significant
+ work for more complex models, and greatly complicates modeling for
+ people not intimately familiar with the details of the fitting code.
+
+ c) There is no simple, robust way to put bounds on values for the
+ variables, or enforce mathematical relationships between the
+ variables. In fact, those optimization methods that do provide
+ bounds, require bounds to be set for all variables with separate
+ arrays that are in the same arbitrary order as variable values.
+ Again, this is acceptable for small or one-off cases, but becomes
+ painful if the fitting model needs to change.
+
+These shortcomings are really do solely to the use of traditional arrays of
+variables, as matches closely the implementation of the Fortran code. The
+lmfit module overcomes these shortcomings by using objects -- a core reason for working with
+Python. The key concept for lmfit is to use :class:`Parameter`
+objects instead of plain floating point numbers as the variables for the
+fit. By using :class:`Parameter` objects (or the closely related
+:class:`Parameters` -- a dictionary of :class:`Parameter` objects), one can
+
+ a) forget about the order of variables and refer to Parameters
+ by meaningful names.
+ b) place bounds on Parameters as attributes, without worrying about order.
+ c) fix Parameters, without having to rewrite the objective function.
+ d) place algebraic constraints on Parameters.
+
+To illustrate the value of this approach, we can rewrite the above example
+as::
+
+ from lmfit import minimize, Parameters
+
+ def residual(params, x, data, eps_data):
+ amp = params['amp'].value
+ pshift = params['phase'].value
+ freq = params['frequency'].value
+ decay = params['decay'].value
+
+ model = amp * sin(x * freq + pshift) * exp(-x*x*decay)
+
+ return (data-model)/eps_data
+
+ params = Parameters()
+ params.add('amp', value=10)
+ params.add('decay', value=0.007)
+ params.add('phase', value=0.2)
+ params.add('frequency', value=3.0)
+
+ out = minimize(residual, params, args=(x, data, eps_data))
+
+
+At first look, we simply replaced a list of values with a dictionary,
+accessed by name -- not a huge improvement. But each of the named
+:class:`Parameter` in the :class:`Parameters` object holds additional
+attributes to modify the value during the fit. For example, Parameters can
+be fixed or bounded. This can be done during definition::
+
+ params = Parameters()
+ params.add('amp', value=10, vary=False)
+ params.add('decay', value=0.007, min=0.0)
+ params.add('phase', value=0.2)
+ params.add('frequency', value=3.0, max=10)
+
+where ``vary=False`` will prevent the value from changing in the fit, and
+``min=0.0`` will set a lower bound on that parameters value). It can also be done
+later by setting the corresponding attributes after they have been
+created::
+
+ params['amp'].vary = False
+ params['decay'].min = 0.10
+
+Importantly, our objective function remains unchanged.
+
+The `params` object can be copied and modified to make many user-level
+changes to the model and fitting process. Of course, most of the
+information about how your data is modeled goes into the objective
+function, but the approach here allows some external control; that is, control by
+the **user** performing the fit, instead of by the author of the
+objective function.
+
+Finally, in addition to the :class:`Parameters` approach to fitting data,
+lmfit allows switching optimization methods without changing
+the objective function, provides tools for writing fitting reports, and
+provides better determination of Parameters confidence levels.
diff --git a/doc/model.rst b/doc/model.rst
index 1e1054b..9b0b595 100644
--- a/doc/model.rst
+++ b/doc/model.rst
@@ -1,1140 +1,1150 @@
-.. _model_chapter:
-
-=================================================
-Modeling Data and Curve Fitting
-=================================================
-
-.. module:: model
-
-A common use of least-squares minimization is *curve fitting*, where one
-has a parametrized model function meant to explain some phenomena and wants
-to adjust the numerical values for the model to most closely match some
-data. With :mod:`scipy`, such problems are commonly solved with
-:func:`scipy.optimize.curve_fit`, which is a wrapper around
-:func:`scipy.optimize.leastsq`. Since Lmfit's :func:`minimize` is also a
-high-level wrapper around :func:`scipy.optimize.leastsq` it can be used for
-curve-fitting problems, but requires more effort than using
-:func:`scipy.optimize.curve_fit`.
-
-Here we discuss lmfit's :class:`Model` class. This takes a model function
--- a function that calculates a model for some data -- and provides methods
-to create parameters for that model and to fit data using that model
-function. This is closer in spirit to :func:`scipy.optimize.curve_fit`,
-but with the advantages of using :class:`Parameters` and lmfit.
-
-In addition to allowing you turn any model function into a curve-fitting
-method, Lmfit also provides canonical definitions for many known line shapes
-such as Gaussian or Lorentzian peaks and Exponential decays that are widely
-used in many scientific domains. These are available in the :mod:`models`
-module that will be discussed in more detail in the next chapter
-(:ref:`builtin_models_chapter`). We mention it here as you may want to
-consult that list before writing your own model. For now, we focus on
-turning python function into high-level fitting models with the
-:class:`Model` class, and using these to fit data.
-
-
-Example: Fit data to Gaussian profile
-================================================
-
-Let's start with a simple and common example of fitting data to a Gaussian
-peak. As we will see, there is a buit-in :class:`GaussianModel` class that
-provides a model function for a Gaussian profile, but here we'll build our
-own. We start with a simple definition of the model function:
-
- >>> from numpy import sqrt, pi, exp, linspace
- >>>
- >>> def gaussian(x, amp, cen, wid):
- ... return amp * exp(-(x-cen)**2 /wid)
- ...
-
-We want to fit this objective function to data :math:`y(x)` represented by the
-arrays ``y`` and ``x``. This can be done easily wit :func:`scipy.optimize.curve_fit`::
-
- >>> from scipy.optimize import curve_fit
- >>>
- >>> x = linspace(-10,10)
- >>> y = y = gaussian(x, 2.33, 0.21, 1.51) + np.random.normal(0, 0.2, len(x))
- >>>
- >>> init_vals = [1, 0, 1] # for [amp, cen, wid]
- >>> best_vals, covar = curve_fit(gaussian, x, y, p0=init_vals)
- >>> print best_vals
-
-
-We sample random data point, make an initial guess of the model
-values, and run :func:`scipy.optimize.curve_fit` with the model function,
-data arrays, and initial guesses. The results returned are the optimal
-values for the parameters and the covariance matrix. It's simple and very
-useful. But it misses the benefits of lmfit.
-
-
-To solve this with lmfit we would have to write an objective function. But
-such a function would be fairly simple (essentially, ``data - model``,
-possibly with some weighting), and we would need to define and use
-appropriately named parameters. Though convenient, it is somewhat of a
-burden to keep the named parameter straight (on the other hand, with
-:func:`scipy.optimize.curve_fit` you are required to remember the parameter
-order). After doing this a few times it appears as a recurring pattern,
-and we can imagine automating this process. That's where the
-:class:`Model` class comes in.
-
-:class:`Model` allows us to easily wrap a model function such as the
-``gaussian`` function. This automatically generate the appropriate
-residual function, and determines the corresponding parameter names from
-the function signature itself::
-
- >>> from lmfit import Model
- >>> gmod = Model(gaussian)
- >>> gmod.param_names
- set(['amp', 'wid', 'cen'])
- >>> gmod.independent_vars)
- ['x']
-
-The Model ``gmod`` knows the names of the parameters and the independent
-variables. By default, the first argument of the function is taken as the
-independent variable, held in :attr:`independent_vars`, and the rest of the
-functions positional arguments (and, in certain cases, keyword arguments --
-see below) are used for Parameter names. Thus, for the ``gaussian``
-function above, the parameters are named ``amp``, ``cen``, and ``wid``, and
-``x`` is the independent variable -- all taken directly from the signature
-of the model function. As we will see below, you can specify what the
-independent variable is, and you can add or alter parameters, too.
-
-The parameters are *not* created when the model is created. The model knows
-what the parameters should be named, but not anything about the scale and
-range of your data. You will normally have to make these parameters and
-assign initial values and other attributes. To help you do this, each
-model has a :meth:`make_params` method that will generate parameters with
-the expected names:
-
- >>> params = gmod.make_params()
-
-This creates the :class:`Parameters` but doesn't necessarily give them
-initial values -- again, the model has no idea what the scale should be.
-You can set initial values for parameters with keyword arguments to
-:meth:`make_params`:
-
-
- >>> params = gmod.make_params(cen=5, amp=200, wid=1)
-
-or assign them (and other parameter properties) after the
-:class:`Parameters` has been created.
-
-A :class:`Model` has several methods associated with it. For example, one
-can use the :meth:`eval` method to evaluate the model or the :meth:`fit`
-method to fit data to this model with a :class:`Parameter` object. Both of
-these methods can take explicit keyword arguments for the parameter values.
-For example, one could use :meth:`eval` to calculate the predicted
-function::
-
- >>> x = linspace(0, 10, 201)
- >>> y = gmod.eval(x=x, amp=10, cen=6.2, wid=0.75)
-
-Admittedly, this a slightly long-winded way to calculate a Gaussian
-function. But now that the model is set up, we can also use its
-:meth:`fit` method to fit this model to data, as with::
-
- >>> result = gmod.fit(y, x=x, amp=5, cen=5, wid=1)
-
-Putting everything together, the script to do such a fit (included in the
-``examples`` folder with the source code) is:
-
-.. literalinclude:: ../examples/doc_model1.py
-
-which is pretty compact and to the point. The returned ``result`` will be
-a :class:`ModelResult` object. As we will see below, this has many
-components, including a :meth:`fit_report` method, which will show::
-
- [[Model]]
- gaussian
- [[Fit Statistics]]
- # function evals = 33
- # data points = 101
- # variables = 3
- chi-square = 3.409
- reduced chi-square = 0.035
- [[Variables]]
- amp: 8.88021829 +/- 0.113594 (1.28%) (init= 5)
- cen: 5.65866102 +/- 0.010304 (0.18%) (init= 5)
- wid: 0.69765468 +/- 0.010304 (1.48%) (init= 1)
- [[Correlations]] (unreported correlations are < 0.100)
- C(amp, wid) = 0.577
-
-The result will also have :attr:`init_fit` for the fit with the initial
-parameter values and a :attr:`best_fit` for the fit with the best fit
-parameter values. These can be used to generate the following plot:
-
-
-.. image:: _images/model_fit1.png
- :target: _images/model_fit1.png
- :width: 50%
-
-which shows the data in blue dots, the best fit as a solid red line, and
-the initial fit as a dashed black line.
-
-Note that the model fitting was really performed with 2 lines of code::
-
- gmod = Model(gaussian)
- result = gmod.fit(y, x=x, amp=5, cen=5, wid=1)
-
-These lines clearly express that we want to turn the ``gaussian`` function
-into a fitting model, and then fit the :math:`y(x)` data to this model,
-starting with values of 5 for ``amp``, 5 for ``cen`` and 1 for ``wid``.
-This is much more expressive than :func:`scipy.optimize.curve_fit`::
-
- best_vals, covar = curve_fit(gaussian, x, y, p0=[5, 5, 1])
-
-In addition, all the other features of lmfit are included:
-:class:`Parameters` can have bounds and constraints and the result is a
-rich object that can be reused to explore the model fit in detail.
-
-
-The :class:`Model` class
-=======================================
-
-The :class:`Model` class provides a general way to wrap a pre-defined
-function as a fitting model.
-
-.. class:: Model(func[, independent_vars=None[, param_names=None[, missing=None[, prefix=''[, name=None[, **kws]]]]]])
-
- Create a model based on the user-supplied function. This uses
- introspection to automatically converting argument names of the
- function to Parameter names.
-
- :param func: model function to be wrapped
- :type func: callable
- :param independent_vars: list of argument names to ``func`` that are independent variables.
- :type independent_vars: ``None`` (default) or list of strings.
- :param param_names: list of argument names to ``func`` that should be made into Parameters.
- :type param_names: ``None`` (default) or list of strings
- :param missing: how to handle missing values.
- :type missing: one of ``None`` (default), 'none', 'drop', or 'raise'.
- :param prefix: prefix to add to all parameter names to distinguish components in a :class:`CompositeModel`.
- :type prefix: string
- :param name: name for the model. When ``None`` (default) the name is the same as the model function (``func``).
- :type name: ``None`` or string.
- :param kws: additional keyword arguments to pass to model function.
-
-
-Of course, the model function will have to return an array that will be the
-same size as the data being modeled. Generally this is handled by also
-specifying one or more independent variables.
-
-
-:class:`Model` class Methods
----------------------------------
-
-.. method:: Model.eval(params=None[, **kws])
-
- evaluate the model function for a set of parameters and inputs.
-
- :param params: parameters to use for fit.
- :type params: ``None`` (default) or Parameters
- :param kws: additional keyword arguments to pass to model function.
- :return: ndarray for model given the parameters and other arguments.
-
- If ``params`` is ``None``, the values for all parameters are expected to
- be provided as keyword arguments. If ``params`` is given, and a keyword
- argument for a parameter value is also given, the keyword argument will
- be used.
-
- Note that all non-parameter arguments for the model function --
- **including all the independent variables!** -- will need to be passed
- in using keyword arguments.
-
-
-.. method:: Model.fit(data[, params=None[, weights=None[, method='leastsq'[, scale_covar=True[, iter_cb=None[, **kws]]]]]])
-
- perform a fit of the model to the ``data`` array with a set of
- parameters.
-
- :param data: array of data to be fitted.
- :type data: ndarray-like
- :param params: parameters to use for fit.
- :type params: ``None`` (default) or Parameters
- :param weights: weights to use for residual calculation in fit.
- :type weights: ``None`` (default) or ndarray-like.
- :param method: name of fitting method to use. See :ref:`fit-methods-label` for details
- :type method: string (default ``leastsq``)
- :param scale_covar: whether to automatically scale covariance matrix (``leastsq`` only)
- :type scale_covar: bool (default ``True``)
- :param iter_cb: function to be called at each fit iteration. See :ref:`fit-itercb-label` for details.
- :type iter_cb: callable or ``None``
- :param verbose: print a message when a new parameter is created due to a *hint*
- :type verbose: bool (default ``True``)
- :param kws: additional keyword arguments to pass to model function.
- :return: :class:`ModelResult` object.
-
- If ``params`` is ``None``, the internal ``params`` will be used. If it
- is supplied, these will replace the internal ones. If supplied,
- ``weights`` will be used to weight the calculated residual so that the
- quantitiy minimized in the least-squares sense is ``weights*(data -
- fit)``. ``weights`` must be an ndarray-like object of same size and
- shape as ``data``.
-
- Note that other arguments for the model function (including all the
- independent variables!) will need to be passed in using keyword
- arguments.
-
-
-.. method:: Model.guess(data, **kws)
-
- Guess starting values for model parameters.
-
- :param data: data array used to guess parameter values
- :type func: ndarray
- :param kws: additional options to pass to model function.
- :return: :class:`Parameters` with guessed initial values for each parameter.
-
- by default this is left to raise a ``NotImplementedError``, but may be
- overwritten by subclasses. Generally, this method should take some
- values for ``data`` and use it to construct reasonable starting values for
- the parameters.
-
-
-.. method:: Model.make_params(**kws)
-
- Create a set of parameters for model.
-
- :param kws: optional keyword/value pairs to set initial values for parameters.
- :return: :class:`Parameters`.
-
- The parameters may or may not have decent initial values for each
- parameter.
-
-
-.. method:: Model.set_param_hint(name, value=None[, min=None[, max=None[, vary=True[, expr=None]]]])
-
- set *hints* to use when creating parameters with :meth:`Model.make_param` for
- the named parameter. This is especially convenient for setting initial
- values. The ``name`` can include the models ``prefix`` or not.
-
- :param name: parameter name.
- :type name: string
- :param value: value for parameter
- :type value: float
- :param min: lower bound for parameter value
- :type min: ``None`` or float
- :param max: upper bound for parameter value
- :type max: ``None`` or float
- :param vary: whether to vary parameter in fit.
- :type vary: boolean
- :param expr: mathematical expression for constraint
- :type expr: string
-
- See :ref:`model_param_hints_section`.
-
-
-:class:`Model` class Attributes
----------------------------------
-
-.. attribute:: func
-
- The model function used to calculate the model.
-
-.. attribute:: independent_vars
-
- list of strings for names of the independent variables.
-
-.. attribute:: missing
-
- describes what to do for missing values. The choices are
-
- * ``None``: Do not check for null or missing values (default)
- * ``'none'``: Do not check for null or missing values.
- * ``'drop'``: Drop null or missing observations in data. If pandas is
- installed, ``pandas.isnull`` is used, otherwise :attr:`numpy.isnan` is used.
- * ``'raise'``: Raise a (more helpful) exception when data contains null
- or missing values.
-
-.. attribute:: name
-
- name of the model, used only in the string representation of the
- model. By default this will be taken from the model function.
-
-.. attribute:: opts
-
- extra keyword arguments to pass to model function. Normally this will
- be determined internally and should not be changed.
-
-.. attribute:: param_hints
-
- Dictionary of parameter hints. See :ref:`model_param_hints_section`.
-
-.. attribute:: param_names
-
- list of strings of parameter names.
-
-.. attribute:: prefix
-
- prefix used for name-mangling of parameter names. The default is ''.
- If a particular :class:`Model` has arguments ``amplitude``,
- ``center``, and ``sigma``, these would become the parameter names.
- Using a prefix of ``g1_`` would convert these parameter names to
- ``g1_amplitude``, ``g1_center``, and ``g1_sigma``. This can be
- essential to avoid name collision in composite models.
-
-
-Determining parameter names and independent variables for a function
------------------------------------------------------------------------
-
-The :class:`Model` created from the supplied function ``func`` will create
-a :class:`Parameters` object, and names are inferred from the function
-arguments, and a residual function is automatically constructed.
-
-
-By default, the independent variable is take as the first argument to the
-function. You can explicitly set this, of course, and will need to if the
-independent variable is not first in the list, or if there are actually more
-than one independent variables.
-
-If not specified, Parameters are constructed from all positional arguments
-and all keyword arguments that have a default value that is numerical, except
-the independent variable, of course. Importantly, the Parameters can be
-modified after creation. In fact, you'll have to do this because none of the
-parameters have valid initial values. You can place bounds and constraints
-on Parameters, or fix their values.
-
-
-
-Explicitly specifying ``independent_vars``
--------------------------------------------------
-
-As we saw for the Gaussian example above, creating a :class:`Model` from a
-function is fairly easy. Let's try another::
-
- >>> def decay(t, tau, N):
- ... return N*np.exp(-t/tau)
- ...
- >>> decay_model = Model(decay)
- >>> print decay_model.independent_vars
- ['t']
- >>> for pname, par in decay_model.params.items():
- ... print pname, par
- ...
- tau <Parameter 'tau', None, bounds=[None:None]>
- N <Parameter 'N', None, bounds=[None:None]>
-
-Here, ``t`` is assumed to be the independent variable because it is the
-first argument to the function. The other function arguments are used to
-create parameters for the model.
-
-If you want ``tau`` to be the independent variable in the above example,
-you can say so::
-
- >>> decay_model = Model(decay, independent_vars=['tau'])
- >>> print decay_model.independent_vars
- ['tau']
- >>> for pname, par in decay_model.params.items():
- ... print pname, par
- ...
- t <Parameter 't', None, bounds=[None:None]>
- N <Parameter 'N', None, bounds=[None:None]>
-
-
-You can also supply multiple values for multi-dimensional functions with
-multiple independent variables. In fact, the meaning of *independent
-variable* here is simple, and based on how it treats arguments of the
-function you are modeling:
-
-independent variable
- a function argument that is not a parameter or otherwise part of the
- model, and that will be required to be explicitly provided as a
- keyword argument for each fit with :meth:`Model.fit` or evaluation
- with :meth:`Model.eval`.
-
-Note that independent variables are not required to be arrays, or even
-floating point numbers.
-
-
-Functions with keyword arguments
------------------------------------------
-
-If the model function had keyword parameters, these would be turned into
-Parameters if the supplied default value was a valid number (but not
-``None``, ``True``, or ``False``).
-
- >>> def decay2(t, tau, N=10, check_positive=False):
- ... if check_small:
- ... arg = abs(t)/max(1.e-9, abs(tau))
- ... else:
- ... arg = t/tau
- ... return N*np.exp(arg)
- ...
- >>> mod = Model(decay2)
- >>> for pname, par in mod.params.items():
- ... print pname, par
- ...
- t <Parameter 't', None, bounds=[None:None]>
- N <Parameter 'N', 10, bounds=[None:None]>
-
-Here, even though ``N`` is a keyword argument to the function, it is turned
-into a parameter, with the default numerical value as its initial value.
-By default, it is permitted to be varied in the fit -- the 10 is taken as
-an initial value, not a fixed value. On the other hand, the
-``check_positive`` keyword argument, was not converted to a parameter
-because it has a boolean default value. In some sense,
-``check_positive`` becomes like an independent variable to the model.
-However, because it has a default value it is not required to be given for
-each model evaluation or fit, as independent variables are.
-
-Defining a ``prefix`` for the Parameters
---------------------------------------------
-
-As we will see in the next chapter when combining models, it is sometimes
-necessary to decorate the parameter names in the model, but still have them
-be correctly used in the underlying model function. This would be
-necessary, for example, if two parameters in a composite model (see
-:ref:`composite_models_section` or examples in the next chapter) would have
-the same name. To avoid this, we can add a ``prefix`` to the
-:class:`Model` which will automatically do this mapping for us.
-
- >>> def myfunc(x, amplitude=1, center=0, sigma=1):
- ...
-
- >>> mod = Model(myfunc, prefix='f1_')
- >>> for pname, par in mod.params.items():
- ... print pname, par
- ...
- f1_amplitude <Parameter 'f1_amplitude', None, bounds=[None:None]>
- f1_center <Parameter 'f1_center', None, bounds=[None:None]>
- f1_sigma <Parameter 'f1_sigma', None, bounds=[None:None]>
-
-You would refer to these parameters as ``f1_amplitude`` and so forth, and
-the model will know to map these to the ``amplitude`` argument of ``myfunc``.
-
-
-Initializing model parameters
------------------------------------------
-
-As mentioned above, the parameters created by :meth:`Model.make_params` are
-generally created with invalid initial values of ``None``. These values
-**must** be initialized in order for the model to be evaluated or used in a
-fit. There are four different ways to do this initialization that can be
-used in any combination:
-
- 1. You can supply initial values in the definition of the model function.
- 2. You can initialize the parameters when creating parameters with :meth:`Model.make_params`.
- 3. You can give parameter hints with :meth:`Model.set_param_hint`.
- 4. You can supply initial values for the parameters when you use the
- :meth:`Model.eval` or :meth:`Model.fit` methods.
-
-Of course these methods can be mixed, allowing you to overwrite initial
-values at any point in the process of defining and using the model.
-
-Initializing values in the function definition
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-To supply initial values for parameters in the definition of the model
-function, you can simply supply a default value::
-
- >>> def myfunc(x, a=1, b=0):
- >>> ...
-
-instead of using::
-
- >>> def myfunc(x, a, b):
- >>> ...
-
-This has the advantage of working at the function level -- all parameters
-with keywords can be treated as options. It also means that some default
-initial value will always be available for the parameter.
-
-
-Initializing values with :meth:`Model.make_params`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-When creating parameters with :meth:`Model.make_params` you can specify initial
-values. To do this, use keyword arguments for the parameter names and
-initial values::
-
- >>> mod = Model(myfunc)
- >>> pars = mod.make_params(a=3, b=0.5)
-
-
-Initializing values by setting parameter hints
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-After a model has been created, but prior to creating parameters with
-:meth:`Model.make_params`, you can set parameter hints. These allows you to set
-not only a default initial value but also to set other parameter attributes
-controlling bounds, whether it is varied in the fit, or a constraint
-expression. To set a parameter hint, you can use :meth:`Model.set_param_hint`,
-as with::
-
- >>> mod = Model(myfunc)
- >>> mod.set_param_hint('a', value = 1.0)
- >>> mod.set_param_hint('b', value = 0.3, min=0, max=1.0)
- >>> pars = mod.make_params()
-
-Parameter hints are discussed in more detail in section
-:ref:`model_param_hints_section`.
-
-
-Initializing values when using a model
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-Finally, you can explicitly supply initial values when using a model. That
-is, as with :meth:`Model.make_params`, you can include values
-as keyword arguments to either the :meth:`Model.eval` or :meth:`Model.fit` methods::
-
- >>> y1 = mod.eval(x=x, a=7.0, b=-2.0)
-
- >>> out = mod.fit(x=x, pars, a=3.0, b=-0.0)
-
-These approaches to initialization provide many opportunities for setting
-initial values for parameters. The methods can be combined, so that you
-can set parameter hints but then change the initial value explicitly with
-:meth:`Model.fit`.
-
-.. _model_param_hints_section:
-
-Using parameter hints
---------------------------------
-
-
-After a model has been created, you can give it hints for how to create
-parameters with :meth:`Model.make_params`. This allows you to set not only a
-default initial value but also to set other parameter attributes
-controlling bounds, whether it is varied in the fit, or a constraint
-expression. To set a parameter hint, you can use :meth:`Model.set_param_hint`,
-as with::
-
- >>> mod = Model(myfunc)
- >>> mod.set_param_hint('a', value = 1.0)
- >>> mod.set_param_hint('b', value = 0.3, min=0, max=1.0)
-
-Parameter hints are stored in a model's :attr:`param_hints` attribute,
-which is simply a nested dictionary::
-
- >>> print mod.param_hints
- {'a': {'value': 1}, 'b': {'max': 1.0, 'value': 0.3, 'min': 0}}
-
-
-You can change this dictionary directly, or with the :meth:`Model.set_param_hint`
-method. Either way, these parameter hints are used by :meth:`Model.make_params`
-when making parameters.
-
-An important feature of parameter hints is that you can force the creation
-of new parameters with parameter hints. This can be useful to make derived
-parameters with constraint expressions. For example to get the full-width
-at half maximum of a Gaussian model, one could use a parameter hint of::
-
- >>> mod = Model(gaussian)
- >>> mod.set_param_hint('fwhm', expr='2.3548*sigma')
-
-
-
-The :class:`ModelResult` class
-=======================================
-
-A :class:`ModelResult` (which had been called `ModelFit` prior to version
-0.9) is the object returned by :meth:`Model.fit`. It is a subclass of
-:class:`Minimizer`, and so contains many of the fit results. Of course, it
-knows the :class:`Model` and the set of :class:`Parameters` used in the
-fit, and it has methods to evaluate the model, to fit the data (or re-fit
-the data with changes to the parameters, or fit with different or modified
-data) and to print out a report for that fit.
-
-While a :class:`Model` encapsulates your model function, it is fairly
-abstract and does not contain the parameters or data used in a particular
-fit. A :class:`ModelResult` *does* contain parameters and data as well as
-methods to alter and re-do fits. Thus the :class:`Model` is the idealized
-model while the :class:`ModelResult` is the messier, more complex (but perhaps
-more useful) object that represents a fit with a set of parameters to data
-with a model.
-
-
-A :class:`ModelResult` has several attributes holding values for fit results,
-and several methods for working with fits. These include statistics
-inherited from :class:`Minimizer` useful for comparing different models,
-includind `chisqr`, `redchi`, `aic`, and `bic`.
-
-.. class:: ModelResult()
-
- Model fit is intended to be created and returned by :meth:`Model.fit`.
-
-
-
-:class:`ModelResult` methods
----------------------------------
-
-These methods are all inherited from :class:`Minimize` or from
-:class:`Model`.
-
-.. method:: ModelResult.eval(**kwargs)
-
- evaluate the model using the best-fit parameters and supplied
- independent variables. The ``**kwargs`` arguments can be used to update
- parameter values and/or independent variables.
-
-
-.. method:: ModelResult.eval_components(**kwargs)
-
- evaluate each component of a :class:`CompositeModel`, returning an
- ordered dictionary of with the values for each component model. The
- returned dictionary will have keys of the model prefix or (if no prefix
- is given), the model name. The ``**kwargs`` arguments can be used to
- update parameter values and/or independent variables.
-
-.. method:: ModelResult.fit(data=None[, params=None[, weights=None[, method=None[, **kwargs]]]])
-
- fit (or re-fit), optionally changing ``data``, ``params``, ``weights``,
- or ``method``, or changing the independent variable(s) with the
- ``**kwargs`` argument. See :meth:`Model.fit` for argument
- descriptions, and note that any value of ``None`` defaults to the last
- used value.
-
-.. method:: ModelResult.fit_report(modelpars=None[, show_correl=True[,`< min_correl=0.1]])
-
- return a printable fit report for the fit with fit statistics, best-fit
- values with uncertainties and correlations. As with :func:`fit_report`.
-
- :param modelpars: Parameters with "Known Values" (optional, default None)
- :param show_correl: whether to show list of sorted correlations [``True``]
- :param min_correl: smallest correlation absolute value to show [0.1]
-
-
-.. method:: ModelResult.conf_interval(**kwargs)
-
- calculate the confidence intervals for the variable parameters using
- :func:`confidence.conf_interval() <lmfit.conf_interval>`. All keyword
- arguments are passed to that function. The result is stored in
- :attr:`ci_out`, and so can be accessed without recalculating them.
-
-.. method:: ModelResult.ci_report(with_offset=True)
-
- return a nicely formatted text report of the confidence intervals, as
- from :func:`ci_report() <lmfit.ci_report>`.
-
-
-.. method:: ModelResult.plot(datafmt='o', fitfmt='-', initfmt='--', yerr=None, numpoints=None, fig=None, data_kws=None, fit_kws=None, init_kws=None, ax_res_kws=None, ax_fit_kws=None, fig_kws=None)
-
- Plot the fit results and residuals using matplotlib, if available. The
- plot will include two panels, one showing the fit residual, and the
- other with the data points, the initial fit curve, and the best-fit
- curve. If the fit model included weights or if ``yerr`` is specified,
- errorbars will also be plotted.
-
- :param datafmt: matplotlib format string for data curve.
- :type datafmt: ``None`` or string.
- :param fitfmt: matplotlib format string for best-fit curve.
- :type fitfmt: ``None`` or string.
- :param initfmt: matplotlib format string for initial curve.
- :type intfmt: ``None`` or string.
- :param yerr: array of uncertainties for data array.
- :type yerr: ``None`` or ndarray.
- :param numpoints: number of points to display
- :type numpoints: ``None`` or integer
- :param fig: matplotlib Figure to plot on.
- :type fig: ``None`` or matplotlib.figure.Figure
- :param data_kws: keyword arguments passed to plot for data curve.
- :type data_kws: ``None`` or dictionary
- :param fit_kws: keyword arguments passed to plot for best-fit curve.
- :type fit_kws: ``None`` or dictionary
- :param init_kws: keyword arguments passed to plot for initial curve.
- :type init_kws: ``None`` or dictionary
- :param ax_res_kws: keyword arguments passed to creation of matplotlib axes for the residual plot.
- :type ax_res_kws: ``None`` or dictionary
- :param ax_fit_kws: keyword arguments passed to creation of matplotlib axes for the fit plot.
- :type ax_fit_kws: ``None`` or dictionary
- :param fig_kws: keyword arguments passed to creation of matplotlib figure.
- :type fig_kws: ``None`` or dictionary
- :returns: matplotlib.figure.Figure
-
- This combines :meth:`ModelResult.plot_fit` and :meth:`ModelResult.plot_residual`.
-
- If ``yerr`` is specified or if the fit model included weights, then
- matplotlib.axes.Axes.errorbar is used to plot the data. If ``yerr`` is
- not specified and the fit includes weights, ``yerr`` set to ``1/self.weights``
-
- If ``fig`` is None then ``matplotlib.pyplot.figure(**fig_kws)`` is called.
-
-.. method:: ModelResult.plot_fit(ax=None, datafmt='o', fitfmt='-', initfmt='--', yerr=None, numpoints=None, data_kws=None, fit_kws=None, init_kws=None, ax_kws=None)
-
- Plot the fit results using matplotlib, if available. The plot will include
- the data points, the initial fit curve, and the best-fit curve. If the fit
- model included weights or if ``yerr`` is specified, errorbars will also
- be plotted.
-
- :param ax: matplotlib axes to plot on.
- :type ax: ``None`` or matplotlib.axes.Axes.
- :param datafmt: matplotlib format string for data curve.
- :type datafmt: ``None`` or string.
- :param fitfmt: matplotlib format string for best-fit curve.
- :type fitfmt: ``None`` or string.
- :param initfmt: matplotlib format string for initial curve.
- :type intfmt: ``None`` or string.
- :param yerr: array of uncertainties for data array.
- :type yerr: ``None`` or ndarray.
- :param numpoints: number of points to display
- :type numpoints: ``None`` or integer
- :param data_kws: keyword arguments passed to plot for data curve.
- :type data_kws: ``None`` or dictionary
- :param fit_kws: keyword arguments passed to plot for best-fit curve.
- :type fit_kws: ``None`` or dictionary
- :param init_kws: keyword arguments passed to plot for initial curve.
- :type init_kws: ``None`` or dictionary
- :param ax_kws: keyword arguments passed to creation of matplotlib axes.
- :type ax_kws: ``None`` or dictionary
- :returns: matplotlib.axes.Axes
-
- For details about plot format strings and keyword arguments see
- documentation of :func:`matplotlib.axes.Axes.plot`.
-
- If ``yerr`` is specified or if the fit model included weights, then
- matplotlib.axes.Axes.errorbar is used to plot the data. If ``yerr`` is
- not specified and the fit includes weights, ``yerr`` set to ``1/self.weights``
-
- If ``ax`` is None then ``matplotlib.pyplot.gca(**ax_kws)`` is called.
-
-.. method:: ModelResult.plot_residuals(ax=None, datafmt='o', yerr=None, data_kws=None, fit_kws=None, ax_kws=None)
-
- Plot the fit residuals (data - fit) using matplotlib. If ``yerr`` is
- supplied or if the model included weights, errorbars will also be plotted.
-
- :param ax: matplotlib axes to plot on.
- :type ax: ``None`` or matplotlib.axes.Axes.
- :param datafmt: matplotlib format string for data curve.
- :type datafmt: ``None`` or string.
- :param yerr: array of uncertainties for data array.
- :type yerr: ``None`` or ndarray.
- :param numpoints: number of points to display
- :type numpoints: ``None`` or integer
- :param data_kws: keyword arguments passed to plot for data curve.
- :type data_kws: ``None`` or dictionary
- :param fit_kws: keyword arguments passed to plot for best-fit curve.
- :type fit_kws: ``None`` or dictionary
- :param ax_kws: keyword arguments passed to creation of matplotlib axes.
- :type ax_kws: ``None`` or dictionary
- :returns: matplotlib.axes.Axes
-
- For details about plot format strings and keyword arguments see
- documentation of :func:`matplotlib.axes.Axes.plot`.
-
- If ``yerr`` is specified or if the fit model included weights, then
- matplotlib.axes.Axes.errorbar is used to plot the data. If ``yerr`` is
- not specified and the fit includes weights, ``yerr`` set to ``1/self.weights``
-
- If ``ax`` is None then ``matplotlib.pyplot.gca(**ax_kws)`` is called.
-
-
-
-
-:class:`ModelResult` attributes
----------------------------------
-
-.. attribute:: aic
-
- floating point best-fit Akaike Information Criterion statistic (see :ref:`fit-results-label`).
-
-.. attribute:: best_fit
-
- ndarray result of model function, evaluated at provided
- independent variables and with best-fit parameters.
-
-.. attribute:: best_values
-
- dictionary with parameter names as keys, and best-fit values as values.
-
-.. attribute:: bic
-
- floating point best-fit Bayesian Information Criterion statistic (see :ref:`fit-results-label`).
-
-.. attribute:: chisqr
-
- floating point best-fit chi-square statistic (see :ref:`fit-results-label`).
-
-.. attribute:: ci_out
-
- confidence interval data (see :ref:`confidence_chapter`) or `None` if
- the confidence intervals have not been calculated.
-
-.. attribute:: covar
-
- ndarray (square) covariance matrix returned from fit.
-
-.. attribute:: data
-
- ndarray of data to compare to model.
-
-.. attribute:: errorbars
-
- boolean for whether error bars were estimated by fit.
-
-.. attribute:: ier
-
- integer returned code from :func:`scipy.optimize.leastsq`.
-
-.. attribute:: init_fit
-
- ndarray result of model function, evaluated at provided
- independent variables and with initial parameters.
-
-.. attribute:: init_params
-
- initial parameters.
-
-.. attribute:: init_values
-
- dictionary with parameter names as keys, and initial values as values.
-
-.. attribute:: iter_cb
-
- optional callable function, to be called at each fit iteration. This
- must take take arguments of ``params, iter, resid, *args, **kws``, where
- ``params`` will have the current parameter values, ``iter`` the
- iteration, ``resid`` the current residual array, and ``*args`` and
- ``**kws`` as passed to the objective function. See :ref:`fit-itercb-label`.
-
-.. attribute:: jacfcn
-
- optional callable function, to be called to calculate jacobian array.
-
-.. attribute:: lmdif_message
-
- string message returned from :func:`scipy.optimize.leastsq`.
-
-.. attribute:: message
-
- string message returned from :func:`minimize`.
-
-.. attribute:: method
-
- string naming fitting method for :func:`minimize`.
-
-.. attribute:: model
-
- instance of :class:`Model` used for model.
-
-.. attribute:: ndata
-
- integer number of data points.
-
-.. attribute:: nfev
-
- integer number of function evaluations used for fit.
-
-.. attribute:: nfree
-
- integer number of free parameters in fit.
-
-.. attribute:: nvarys
-
- integer number of independent, freely varying variables in fit.
-
-.. attribute:: params
-
- Parameters used in fit. Will have best-fit values.
-
-.. attribute:: redchi
-
- floating point reduced chi-square statistic (see :ref:`fit-results-label`).
-
-.. attribute:: residual
-
- ndarray for residual.
-
-.. attribute:: scale_covar
-
- boolean flag for whether to automatically scale covariance matrix.
-
-.. attribute:: success
-
- boolean value of whether fit succeeded.
-
-.. attribute:: weights
-
- ndarray (or ``None``) of weighting values to be used in fit. If not
- ``None``, it will be used as a multiplicative factor of the residual
- array, so that ``weights*(data - fit)`` is minimized in the
- least-squares sense.
-
-.. index:: Composite models
-
-.. _composite_models_section:
-
-
-Composite Models : adding (or multiplying) Models
-==============================================================
-
-One of the more interesting features of the :class:`Model` class is that
-Models can be added together or combined with basic algebraic operations
-(add, subtract, multiply, and divide) to give a composite model. The
-composite model will have parameters from each of the component models,
-with all parameters being available to influence the whole model. This
-ability to combine models will become even more useful in the next chapter,
-when pre-built subclasses of :class:`Model` are discussed. For now, we'll
-consider a simple example, and build a model of a Gaussian plus a line, as
-to model a peak with a background. For such a simple problem, we could just
-build a model that included both components::
-
- def gaussian_plus_line(x, amp, cen, wid, slope, intercept):
- "line + 1-d gaussian"
-
- gauss = (amp/(sqrt(2*pi)*wid)) * exp(-(x-cen)**2 /(2*wid**2))
- line = slope * x + intercept
- return gauss + line
-
-and use that with::
-
- mod = Model(gaussian_plus_line)
-
-But we already had a function for a gaussian function, and maybe we'll
-discover that a linear background isn't sufficient which would mean the
-model function would have to be changed. As an alternative we could define
-a linear function::
-
- def line(x, slope, intercept):
- "a line"
- return slope * x + intercept
-
-and build a composite model with just::
-
- mod = Model(gaussian) + Model(line)
-
-This model has parameters for both component models, and can be used as:
-
-.. literalinclude:: ../examples/doc_model2.py
-
-which prints out the results::
-
- [[Model]]
- (Model(gaussian) + Model(line))
- [[Fit Statistics]]
- # function evals = 44
- # data points = 101
- # variables = 5
- chi-square = 2.579
- reduced chi-square = 0.027
- [[Variables]]
- amp: 8.45931061 +/- 0.124145 (1.47%) (init= 5)
- cen: 5.65547872 +/- 0.009176 (0.16%) (init= 5)
- intercept: -0.96860201 +/- 0.033522 (3.46%) (init= 1)
- slope: 0.26484403 +/- 0.005748 (2.17%) (init= 0)
- wid: 0.67545523 +/- 0.009916 (1.47%) (init= 1)
- [[Correlations]] (unreported correlations are < 0.100)
- C(amp, wid) = 0.666
- C(cen, intercept) = 0.129
-
-
-and shows the plot on the left.
-
-.. _figModel2:
-
- .. image:: _images/model_fit2.png
- :target: _images/model_fit2.png
- :width: 48%
- .. image:: _images/model_fit2a.png
- :target: _images/model_fit2a.png
- :width: 48%
-
-
-On the left, data is shown in blue dots, the total fit is shown in solid
-red line, and the initial fit is shown as a black dashed line. In the
-figure on the right, the data is again shown in blue dots, and the Gaussian
-component shown as a black dashed line, and the linear component shown as a
-red dashed line. These components were generated after the fit using the
-Models :meth:`ModelResult.eval_components` method of the `result`::
-
- comps = result.eval_components()
-
-which returns a dictionary of the components, using keys of the model name
-(or `prefix` if that is set). This will use the parameter values in
-``result.params`` and the independent variables (``x``) used during the
-fit. Note that while the :class:`ModelResult` held in `result` does store the
-best parameters and the best estimate of the model in ``result.best_fit``,
-the original model and parameters in ``pars`` are left unaltered.
-
-You can apply this composite model to other data sets, or evaluate the
-model at other values of ``x``. You may want to do this to give a finer or
-coarser spacing of data point, or to extrapolate the model outside the
-fitting range. This can be done with::
-
- xwide = np.linspace(-5, 25, 3001)
- predicted = mod.eval(x=xwide)
-
-In this example, the argument names for the model functions do not overlap.
-If they had, the ``prefix`` argument to :class:`Model` would have allowed
-us to identify which parameter went with which component model. As we will
-see in the next chapter, using composite models with the built-in models
-provides a simple way to build up complex models.
-
-.. class:: CompositeModel(left, right, op[, **kws])
-
- Create a composite model from two models (`left` and `right` and an
- binary operator (`op`). Additional keywords are passed to
- :class:`Model`.
-
- :param left: left-hand side Model
- :type left: :class:`Model`
- :param right: right-hand side Model
- :type right: :class:`Model`
- :param op: binary operator
- :type op: callable, and taking 2 arguments (`left` and `right`).
-
-Normally, one does not have to explicitly create a :class:`CompositeModel`,
-as doing::
-
- mod = Model(fcn1) + Model(fcn2) * Model(fcn3)
-
-will automatically create a :class:`CompositeModel`. In this example,
-`mod.left` will be `Model(fcn1)`, `mod.op` will be :meth:`operator.add`,
-and `mod.right` will be another CompositeModel that has a `left` attribute
-of `Model(fcn2)`, an `op` of :meth:`operator.mul`, and a `right` of
-`Model(fcn3)`.
-
-If you want to use a binary operator other than add, subtract, multiply, or
-divide that are supported through normal Python syntax, you'll need to
-explicitly create a :class:`CompositeModel` with the appropriate binary
-operator. For example, to convolve two models, you could define a simple
-convolution function, perhaps as::
-
- import numpy as np
- def convolve(dat, kernel):
- # simple convolution
- npts = min(len(dat), len(kernel))
- pad = np.ones(npts)
- tmp = np.concatenate((pad*dat[0], dat, pad*dat[-1]))
- out = np.convolve(tmp, kernel, mode='valid')
- noff = int((len(out) - npts)/2)
- return (out[noff:])[:npts]
-
-which extends the data in both directions so that the convolving kernel
-function gives a valid result over the data range. Because this function
-takes two array arguments and returns an array, it can be used as the
-binary operator. A full script using this technique is here:
-
-.. literalinclude:: ../examples/doc_model3.py
-
-which prints out the results::
-
- [[Model]]
- (Model(jump) <function convolve at 0x109ee4488> Model(gaussian))
- [[Fit Statistics]]
- # function evals = 25
- # data points = 201
- # variables = 3
- chi-square = 21.692
- reduced chi-square = 0.110
- [[Variables]]
- amplitude: 0.62106099 +/- 0.001783 (0.29%) (init= 1)
- center: 4.49913218 +/- 0.009373 (0.21%) (init= 3.5)
- mid: 5 (fixed)
- sigma: 0.61936067 +/- 0.012977 (2.10%) (init= 1)
- [[Correlations]] (unreported correlations are < 0.100)
- C(amplitude, center) = 0.336
- C(amplitude, sigma) = 0.274
-
-and shows the plots:
-
-.. _figModel3:
-
- .. image:: _images/model_fit3a.png
- :target: _images/model_fit3a.png
- :width: 48%
- .. image:: _images/model_fit3b.png
- :target: _images/model_fit3b.png
- :width: 48%
-
-Using composite models with built-in or custom operators allows you to
-build complex models from testable sub-components.
+.. _model_chapter:
+
+=================================================
+Modeling Data and Curve Fitting
+=================================================
+
+.. module:: model
+
+A common use of least-squares minimization is *curve fitting*, where one
+has a parametrized model function meant to explain some phenomena and wants
+to adjust the numerical values for the model to most closely match some
+data. With :mod:`scipy`, such problems are commonly solved with
+:scipydoc:`scipy.optimize.curve_fit`, which is a wrapper around
+:scipydoc:`scipy.optimize.leastsq`. Since Lmfit's :func:`minimize` is also
+a high-level wrapper around :scipydoc:`scipy.optimize.leastsq` it can be used
+for curve-fitting problems, but requires more effort than using
+:scipydoc:`scipy.optimize.curve_fit`.
+
+
+Here we discuss lmfit's :class:`Model` class. This takes a model function
+-- a function that calculates a model for some data -- and provides methods
+to create parameters for that model and to fit data using that model
+function. This is closer in spirit to :scipydoc:`scipy.optimize.curve_fit`,
+but with the advantages of using :class:`Parameters` and lmfit.
+
+In addition to allowing you turn any model function into a curve-fitting
+method, Lmfit also provides canonical definitions for many known line shapes
+such as Gaussian or Lorentzian peaks and Exponential decays that are widely
+used in many scientific domains. These are available in the :mod:`models`
+module that will be discussed in more detail in the next chapter
+(:ref:`builtin_models_chapter`). We mention it here as you may want to
+consult that list before writing your own model. For now, we focus on
+turning python function into high-level fitting models with the
+:class:`Model` class, and using these to fit data.
+
+
+Example: Fit data to Gaussian profile
+================================================
+
+Let's start with a simple and common example of fitting data to a Gaussian
+peak. As we will see, there is a buit-in :class:`GaussianModel` class that
+provides a model function for a Gaussian profile, but here we'll build our
+own. We start with a simple definition of the model function:
+
+ >>> from numpy import sqrt, pi, exp, linspace
+ >>>
+ >>> def gaussian(x, amp, cen, wid):
+ ... return amp * exp(-(x-cen)**2 /wid)
+ ...
+
+We want to fit this objective function to data :math:`y(x)` represented by the
+arrays ``y`` and ``x``. This can be done easily with :scipydoc:`optimize.curve_fit`::
+
+ >>> from scipy.optimize import curve_fit
+ >>>
+ >>> x = linspace(-10,10)
+ >>> y = y = gaussian(x, 2.33, 0.21, 1.51) + np.random.normal(0, 0.2, len(x))
+ >>>
+ >>> init_vals = [1, 0, 1] # for [amp, cen, wid]
+ >>> best_vals, covar = curve_fit(gaussian, x, y, p0=init_vals)
+ >>> print best_vals
+
+
+We sample random data point, make an initial guess of the model
+values, and run :scipydoc:`optimize.curve_fit` with the model function,
+data arrays, and initial guesses. The results returned are the optimal
+values for the parameters and the covariance matrix. It's simple and very
+useful. But it misses the benefits of lmfit.
+
+
+To solve this with lmfit we would have to write an objective function. But
+such a function would be fairly simple (essentially, ``data - model``,
+possibly with some weighting), and we would need to define and use
+appropriately named parameters. Though convenient, it is somewhat of a
+burden to keep the named parameter straight (on the other hand, with
+:scipydoc:`optimize.curve_fit` you are required to remember the parameter
+order). After doing this a few times it appears as a recurring pattern,
+and we can imagine automating this process. That's where the
+:class:`Model` class comes in.
+
+:class:`Model` allows us to easily wrap a model function such as the
+``gaussian`` function. This automatically generate the appropriate
+residual function, and determines the corresponding parameter names from
+the function signature itself::
+
+ >>> from lmfit import Model
+ >>> gmod = Model(gaussian)
+ >>> gmod.param_names
+ set(['amp', 'wid', 'cen'])
+ >>> gmod.independent_vars)
+ ['x']
+
+The Model ``gmod`` knows the names of the parameters and the independent
+variables. By default, the first argument of the function is taken as the
+independent variable, held in :attr:`independent_vars`, and the rest of the
+functions positional arguments (and, in certain cases, keyword arguments --
+see below) are used for Parameter names. Thus, for the ``gaussian``
+function above, the parameters are named ``amp``, ``cen``, and ``wid``, and
+``x`` is the independent variable -- all taken directly from the signature
+of the model function. As we will see below, you can specify what the
+independent variable is, and you can add or alter parameters, too.
+
+The parameters are *not* created when the model is created. The model knows
+what the parameters should be named, but not anything about the scale and
+range of your data. You will normally have to make these parameters and
+assign initial values and other attributes. To help you do this, each
+model has a :meth:`make_params` method that will generate parameters with
+the expected names:
+
+ >>> params = gmod.make_params()
+
+This creates the :class:`Parameters` but doesn't necessarily give them
+initial values -- again, the model has no idea what the scale should be.
+You can set initial values for parameters with keyword arguments to
+:meth:`make_params`:
+
+
+ >>> params = gmod.make_params(cen=5, amp=200, wid=1)
+
+or assign them (and other parameter properties) after the
+:class:`Parameters` has been created.
+
+A :class:`Model` has several methods associated with it. For example, one
+can use the :meth:`eval` method to evaluate the model or the :meth:`fit`
+method to fit data to this model with a :class:`Parameter` object. Both of
+these methods can take explicit keyword arguments for the parameter values.
+For example, one could use :meth:`eval` to calculate the predicted
+function::
+
+ >>> x = linspace(0, 10, 201)
+ >>> y = gmod.eval(x=x, amp=10, cen=6.2, wid=0.75)
+
+Admittedly, this a slightly long-winded way to calculate a Gaussian
+function. But now that the model is set up, we can also use its
+:meth:`fit` method to fit this model to data, as with::
+
+ >>> result = gmod.fit(y, x=x, amp=5, cen=5, wid=1)
+
+Putting everything together, the script to do such a fit (included in the
+``examples`` folder with the source code) is:
+
+.. literalinclude:: ../examples/doc_model1.py
+
+which is pretty compact and to the point. The returned ``result`` will be
+a :class:`ModelResult` object. As we will see below, this has many
+components, including a :meth:`fit_report` method, which will show::
+
+ [[Model]]
+ gaussian
+ [[Fit Statistics]]
+ # function evals = 33
+ # data points = 101
+ # variables = 3
+ chi-square = 3.409
+ reduced chi-square = 0.035
+ Akaike info crit = -333.218
+ Bayesian info crit = -325.373
+ [[Variables]]
+ amp: 8.88021829 +/- 0.113594 (1.28%) (init= 5)
+ cen: 5.65866102 +/- 0.010304 (0.18%) (init= 5)
+ wid: 0.69765468 +/- 0.010304 (1.48%) (init= 1)
+ [[Correlations]] (unreported correlations are < 0.100)
+ C(amp, wid) = 0.577
+
+The result will also have :attr:`init_fit` for the fit with the initial
+parameter values and a :attr:`best_fit` for the fit with the best fit
+parameter values. These can be used to generate the following plot:
+
+
+.. image:: _images/model_fit1.png
+ :target: _images/model_fit1.png
+ :width: 50%
+
+which shows the data in blue dots, the best fit as a solid red line, and
+the initial fit as a dashed black line.
+
+Note that the model fitting was really performed with 2 lines of code::
+
+ gmod = Model(gaussian)
+ result = gmod.fit(y, x=x, amp=5, cen=5, wid=1)
+
+These lines clearly express that we want to turn the ``gaussian`` function
+into a fitting model, and then fit the :math:`y(x)` data to this model,
+starting with values of 5 for ``amp``, 5 for ``cen`` and 1 for ``wid``.
+This is much more expressive than :scipydoc:`optimize.curve_fit`::
+
+ best_vals, covar = curve_fit(gaussian, x, y, p0=[5, 5, 1])
+
+In addition, all the other features of lmfit are included:
+:class:`Parameters` can have bounds and constraints and the result is a
+rich object that can be reused to explore the model fit in detail.
+
+
+The :class:`Model` class
+=======================================
+
+The :class:`Model` class provides a general way to wrap a pre-defined
+function as a fitting model.
+
+.. class:: Model(func[, independent_vars=None[, param_names=None[, missing=None[, prefix=''[, name=None[, **kws]]]]]])
+
+ Create a model based on the user-supplied function. This uses
+ introspection to automatically converting argument names of the
+ function to Parameter names.
+
+ :param func: model function to be wrapped
+ :type func: callable
+ :param independent_vars: list of argument names to ``func`` that are independent variables.
+ :type independent_vars: ``None`` (default) or list of strings.
+ :param param_names: list of argument names to ``func`` that should be made into Parameters.
+ :type param_names: ``None`` (default) or list of strings
+ :param missing: how to handle missing values.
+ :type missing: one of ``None`` (default), 'none', 'drop', or 'raise'.
+ :param prefix: prefix to add to all parameter names to distinguish components in a :class:`CompositeModel`.
+ :type prefix: string
+ :param name: name for the model. When ``None`` (default) the name is the same as the model function (``func``).
+ :type name: ``None`` or string.
+ :param kws: additional keyword arguments to pass to model function.
+
+
+Of course, the model function will have to return an array that will be the
+same size as the data being modeled. Generally this is handled by also
+specifying one or more independent variables.
+
+
+:class:`Model` class Methods
+---------------------------------
+
+.. method:: Model.eval(params=None[, **kws])
+
+ evaluate the model function for a set of parameters and inputs.
+
+ :param params: parameters to use for fit.
+ :type params: ``None`` (default) or Parameters
+ :param kws: additional keyword arguments to pass to model function.
+ :return: ndarray for model given the parameters and other arguments.
+
+ If ``params`` is ``None``, the values for all parameters are expected to
+ be provided as keyword arguments. If ``params`` is given, and a keyword
+ argument for a parameter value is also given, the keyword argument will
+ be used.
+
+ Note that all non-parameter arguments for the model function --
+ **including all the independent variables!** -- will need to be passed
+ in using keyword arguments.
+
+
+.. method:: Model.fit(data[, params=None[, weights=None[, method='leastsq'[, scale_covar=True[, iter_cb=None[, **kws]]]]]])
+
+ perform a fit of the model to the ``data`` array with a set of
+ parameters.
+
+ :param data: array of data to be fitted.
+ :type data: ndarray-like
+ :param params: parameters to use for fit.
+ :type params: ``None`` (default) or Parameters
+ :param weights: weights to use for residual calculation in fit.
+ :type weights: ``None`` (default) or ndarray-like.
+ :param method: name of fitting method to use. See :ref:`fit-methods-label` for details
+ :type method: string (default ``leastsq``)
+ :param scale_covar: whether to automatically scale covariance matrix (``leastsq`` only)
+ :type scale_covar: bool (default ``True``)
+ :param iter_cb: function to be called at each fit iteration. See :ref:`fit-itercb-label` for details.
+ :type iter_cb: callable or ``None``
+ :param verbose: print a message when a new parameter is created due to a *hint*
+ :type verbose: bool (default ``True``)
+ :param kws: additional keyword arguments to pass to model function.
+ :return: :class:`ModelResult` object.
+
+ If ``params`` is ``None``, the internal ``params`` will be used. If it
+ is supplied, these will replace the internal ones. If supplied,
+ ``weights`` will be used to weight the calculated residual so that the
+ quantity minimized in the least-squares sense is ``weights*(data -
+ fit)``. ``weights`` must be an ndarray-like object of same size and
+ shape as ``data``.
+
+ Note that other arguments for the model function (including all the
+ independent variables!) will need to be passed in using keyword
+ arguments.
+
+
+.. method:: Model.guess(data, **kws)
+
+ Guess starting values for model parameters.
+
+ :param data: data array used to guess parameter values
+ :type func: ndarray
+ :param kws: additional options to pass to model function.
+ :return: :class:`Parameters` with guessed initial values for each parameter.
+
+ by default this is left to raise a ``NotImplementedError``, but may be
+ overwritten by subclasses. Generally, this method should take some
+ values for ``data`` and use it to construct reasonable starting values for
+ the parameters.
+
+
+.. method:: Model.make_params(**kws)
+
+ Create a set of parameters for model.
+
+ :param kws: optional keyword/value pairs to set initial values for parameters.
+ :return: :class:`Parameters`.
+
+ The parameters may or may not have decent initial values for each
+ parameter.
+
+
+.. method:: Model.set_param_hint(name, value=None[, min=None[, max=None[, vary=True[, expr=None]]]])
+
+ set *hints* to use when creating parameters with :meth:`Model.make_param` for
+ the named parameter. This is especially convenient for setting initial
+ values. The ``name`` can include the models ``prefix`` or not.
+
+ :param name: parameter name.
+ :type name: string
+ :param value: value for parameter
+ :type value: float
+ :param min: lower bound for parameter value
+ :type min: ``None`` or float
+ :param max: upper bound for parameter value
+ :type max: ``None`` or float
+ :param vary: whether to vary parameter in fit.
+ :type vary: boolean
+ :param expr: mathematical expression for constraint
+ :type expr: string
+
+ See :ref:`model_param_hints_section`.
+
+
+.. automethod:: lmfit.model.Model.print_param_hints
+
+
+:class:`Model` class Attributes
+---------------------------------
+
+.. attribute:: func
+
+ The model function used to calculate the model.
+
+.. attribute:: independent_vars
+
+ list of strings for names of the independent variables.
+
+.. attribute:: missing
+
+ describes what to do for missing values. The choices are
+
+ * ``None``: Do not check for null or missing values (default)
+ * ``'none'``: Do not check for null or missing values.
+ * ``'drop'``: Drop null or missing observations in data. If pandas is
+ installed, ``pandas.isnull`` is used, otherwise :attr:`numpy.isnan` is used.
+ * ``'raise'``: Raise a (more helpful) exception when data contains null
+ or missing values.
+
+.. attribute:: name
+
+ name of the model, used only in the string representation of the
+ model. By default this will be taken from the model function.
+
+.. attribute:: opts
+
+ extra keyword arguments to pass to model function. Normally this will
+ be determined internally and should not be changed.
+
+.. attribute:: param_hints
+
+ Dictionary of parameter hints. See :ref:`model_param_hints_section`.
+
+.. attribute:: param_names
+
+ list of strings of parameter names.
+
+.. attribute:: prefix
+
+ prefix used for name-mangling of parameter names. The default is ''.
+ If a particular :class:`Model` has arguments ``amplitude``,
+ ``center``, and ``sigma``, these would become the parameter names.
+ Using a prefix of ``g1_`` would convert these parameter names to
+ ``g1_amplitude``, ``g1_center``, and ``g1_sigma``. This can be
+ essential to avoid name collision in composite models.
+
+
+Determining parameter names and independent variables for a function
+-----------------------------------------------------------------------
+
+The :class:`Model` created from the supplied function ``func`` will create
+a :class:`Parameters` object, and names are inferred from the function
+arguments, and a residual function is automatically constructed.
+
+
+By default, the independent variable is take as the first argument to the
+function. You can explicitly set this, of course, and will need to if the
+independent variable is not first in the list, or if there are actually more
+than one independent variables.
+
+If not specified, Parameters are constructed from all positional arguments
+and all keyword arguments that have a default value that is numerical, except
+the independent variable, of course. Importantly, the Parameters can be
+modified after creation. In fact, you'll have to do this because none of the
+parameters have valid initial values. You can place bounds and constraints
+on Parameters, or fix their values.
+
+
+
+Explicitly specifying ``independent_vars``
+-------------------------------------------------
+
+As we saw for the Gaussian example above, creating a :class:`Model` from a
+function is fairly easy. Let's try another::
+
+ >>> def decay(t, tau, N):
+ ... return N*np.exp(-t/tau)
+ ...
+ >>> decay_model = Model(decay)
+ >>> print decay_model.independent_vars
+ ['t']
+ >>> for pname, par in decay_model.params.items():
+ ... print pname, par
+ ...
+ tau <Parameter 'tau', None, bounds=[None:None]>
+ N <Parameter 'N', None, bounds=[None:None]>
+
+Here, ``t`` is assumed to be the independent variable because it is the
+first argument to the function. The other function arguments are used to
+create parameters for the model.
+
+If you want ``tau`` to be the independent variable in the above example,
+you can say so::
+
+ >>> decay_model = Model(decay, independent_vars=['tau'])
+ >>> print decay_model.independent_vars
+ ['tau']
+ >>> for pname, par in decay_model.params.items():
+ ... print pname, par
+ ...
+ t <Parameter 't', None, bounds=[None:None]>
+ N <Parameter 'N', None, bounds=[None:None]>
+
+
+You can also supply multiple values for multi-dimensional functions with
+multiple independent variables. In fact, the meaning of *independent
+variable* here is simple, and based on how it treats arguments of the
+function you are modeling:
+
+independent variable
+ a function argument that is not a parameter or otherwise part of the
+ model, and that will be required to be explicitly provided as a
+ keyword argument for each fit with :meth:`Model.fit` or evaluation
+ with :meth:`Model.eval`.
+
+Note that independent variables are not required to be arrays, or even
+floating point numbers.
+
+
+Functions with keyword arguments
+-----------------------------------------
+
+If the model function had keyword parameters, these would be turned into
+Parameters if the supplied default value was a valid number (but not
+``None``, ``True``, or ``False``).
+
+ >>> def decay2(t, tau, N=10, check_positive=False):
+ ... if check_small:
+ ... arg = abs(t)/max(1.e-9, abs(tau))
+ ... else:
+ ... arg = t/tau
+ ... return N*np.exp(arg)
+ ...
+ >>> mod = Model(decay2)
+ >>> for pname, par in mod.params.items():
+ ... print pname, par
+ ...
+ t <Parameter 't', None, bounds=[None:None]>
+ N <Parameter 'N', 10, bounds=[None:None]>
+
+Here, even though ``N`` is a keyword argument to the function, it is turned
+into a parameter, with the default numerical value as its initial value.
+By default, it is permitted to be varied in the fit -- the 10 is taken as
+an initial value, not a fixed value. On the other hand, the
+``check_positive`` keyword argument, was not converted to a parameter
+because it has a boolean default value. In some sense,
+``check_positive`` becomes like an independent variable to the model.
+However, because it has a default value it is not required to be given for
+each model evaluation or fit, as independent variables are.
+
+Defining a ``prefix`` for the Parameters
+--------------------------------------------
+
+As we will see in the next chapter when combining models, it is sometimes
+necessary to decorate the parameter names in the model, but still have them
+be correctly used in the underlying model function. This would be
+necessary, for example, if two parameters in a composite model (see
+:ref:`composite_models_section` or examples in the next chapter) would have
+the same name. To avoid this, we can add a ``prefix`` to the
+:class:`Model` which will automatically do this mapping for us.
+
+ >>> def myfunc(x, amplitude=1, center=0, sigma=1):
+ ...
+
+ >>> mod = Model(myfunc, prefix='f1_')
+ >>> for pname, par in mod.params.items():
+ ... print pname, par
+ ...
+ f1_amplitude <Parameter 'f1_amplitude', None, bounds=[None:None]>
+ f1_center <Parameter 'f1_center', None, bounds=[None:None]>
+ f1_sigma <Parameter 'f1_sigma', None, bounds=[None:None]>
+
+You would refer to these parameters as ``f1_amplitude`` and so forth, and
+the model will know to map these to the ``amplitude`` argument of ``myfunc``.
+
+
+Initializing model parameters
+-----------------------------------------
+
+As mentioned above, the parameters created by :meth:`Model.make_params` are
+generally created with invalid initial values of ``None``. These values
+**must** be initialized in order for the model to be evaluated or used in a
+fit. There are four different ways to do this initialization that can be
+used in any combination:
+
+ 1. You can supply initial values in the definition of the model function.
+ 2. You can initialize the parameters when creating parameters with :meth:`Model.make_params`.
+ 3. You can give parameter hints with :meth:`Model.set_param_hint`.
+ 4. You can supply initial values for the parameters when you use the
+ :meth:`Model.eval` or :meth:`Model.fit` methods.
+
+Of course these methods can be mixed, allowing you to overwrite initial
+values at any point in the process of defining and using the model.
+
+Initializing values in the function definition
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+To supply initial values for parameters in the definition of the model
+function, you can simply supply a default value::
+
+ >>> def myfunc(x, a=1, b=0):
+ >>> ...
+
+instead of using::
+
+ >>> def myfunc(x, a, b):
+ >>> ...
+
+This has the advantage of working at the function level -- all parameters
+with keywords can be treated as options. It also means that some default
+initial value will always be available for the parameter.
+
+
+Initializing values with :meth:`Model.make_params`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+When creating parameters with :meth:`Model.make_params` you can specify initial
+values. To do this, use keyword arguments for the parameter names and
+initial values::
+
+ >>> mod = Model(myfunc)
+ >>> pars = mod.make_params(a=3, b=0.5)
+
+
+Initializing values by setting parameter hints
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+After a model has been created, but prior to creating parameters with
+:meth:`Model.make_params`, you can set parameter hints. These allows you to set
+not only a default initial value but also to set other parameter attributes
+controlling bounds, whether it is varied in the fit, or a constraint
+expression. To set a parameter hint, you can use :meth:`Model.set_param_hint`,
+as with::
+
+ >>> mod = Model(myfunc)
+ >>> mod.set_param_hint('a', value = 1.0)
+ >>> mod.set_param_hint('b', value = 0.3, min=0, max=1.0)
+ >>> pars = mod.make_params()
+
+Parameter hints are discussed in more detail in section
+:ref:`model_param_hints_section`.
+
+
+Initializing values when using a model
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Finally, you can explicitly supply initial values when using a model. That
+is, as with :meth:`Model.make_params`, you can include values
+as keyword arguments to either the :meth:`Model.eval` or :meth:`Model.fit` methods::
+
+ >>> y1 = mod.eval(x=x, a=7.0, b=-2.0)
+
+ >>> out = mod.fit(x=x, pars, a=3.0, b=-0.0)
+
+These approaches to initialization provide many opportunities for setting
+initial values for parameters. The methods can be combined, so that you
+can set parameter hints but then change the initial value explicitly with
+:meth:`Model.fit`.
+
+.. _model_param_hints_section:
+
+Using parameter hints
+--------------------------------
+
+
+After a model has been created, you can give it hints for how to create
+parameters with :meth:`Model.make_params`. This allows you to set not only a
+default initial value but also to set other parameter attributes
+controlling bounds, whether it is varied in the fit, or a constraint
+expression. To set a parameter hint, you can use :meth:`Model.set_param_hint`,
+as with::
+
+ >>> mod = Model(myfunc)
+ >>> mod.set_param_hint('a', value = 1.0)
+ >>> mod.set_param_hint('b', value = 0.3, min=0, max=1.0)
+
+Parameter hints are stored in a model's :attr:`param_hints` attribute,
+which is simply a nested dictionary::
+
+ >>> print mod.param_hints
+ {'a': {'value': 1}, 'b': {'max': 1.0, 'value': 0.3, 'min': 0}}
+
+
+You can change this dictionary directly, or with the :meth:`Model.set_param_hint`
+method. Either way, these parameter hints are used by :meth:`Model.make_params`
+when making parameters.
+
+An important feature of parameter hints is that you can force the creation
+of new parameters with parameter hints. This can be useful to make derived
+parameters with constraint expressions. For example to get the full-width
+at half maximum of a Gaussian model, one could use a parameter hint of::
+
+ >>> mod = Model(gaussian)
+ >>> mod.set_param_hint('fwhm', expr='2.3548*sigma')
+
+
+
+The :class:`ModelResult` class
+=======================================
+
+A :class:`ModelResult` (which had been called `ModelFit` prior to version
+0.9) is the object returned by :meth:`Model.fit`. It is a subclass of
+:class:`Minimizer`, and so contains many of the fit results. Of course, it
+knows the :class:`Model` and the set of :class:`Parameters` used in the
+fit, and it has methods to evaluate the model, to fit the data (or re-fit
+the data with changes to the parameters, or fit with different or modified
+data) and to print out a report for that fit.
+
+While a :class:`Model` encapsulates your model function, it is fairly
+abstract and does not contain the parameters or data used in a particular
+fit. A :class:`ModelResult` *does* contain parameters and data as well as
+methods to alter and re-do fits. Thus the :class:`Model` is the idealized
+model while the :class:`ModelResult` is the messier, more complex (but perhaps
+more useful) object that represents a fit with a set of parameters to data
+with a model.
+
+
+A :class:`ModelResult` has several attributes holding values for fit results,
+and several methods for working with fits. These include statistics
+inherited from :class:`Minimizer` useful for comparing different models,
+including `chisqr`, `redchi`, `aic`, and `bic`.
+
+.. class:: ModelResult()
+
+ Model fit is intended to be created and returned by :meth:`Model.fit`.
+
+
+
+:class:`ModelResult` methods
+---------------------------------
+
+These methods are all inherited from :class:`Minimize` or from
+:class:`Model`.
+
+.. method:: ModelResult.eval(**kwargs)
+
+ evaluate the model using the best-fit parameters and supplied
+ independent variables. The ``**kwargs`` arguments can be used to update
+ parameter values and/or independent variables.
+
+
+.. method:: ModelResult.eval_components(**kwargs)
+
+ evaluate each component of a :class:`CompositeModel`, returning an
+ ordered dictionary of with the values for each component model. The
+ returned dictionary will have keys of the model prefix or (if no prefix
+ is given), the model name. The ``**kwargs`` arguments can be used to
+ update parameter values and/or independent variables.
+
+.. method:: ModelResult.fit(data=None[, params=None[, weights=None[, method=None[, **kwargs]]]])
+
+ fit (or re-fit), optionally changing ``data``, ``params``, ``weights``,
+ or ``method``, or changing the independent variable(s) with the
+ ``**kwargs`` argument. See :meth:`Model.fit` for argument
+ descriptions, and note that any value of ``None`` defaults to the last
+ used value.
+
+.. method:: ModelResult.fit_report(modelpars=None[, show_correl=True[,`< min_correl=0.1]])
+
+ return a printable fit report for the fit with fit statistics, best-fit
+ values with uncertainties and correlations. As with :func:`fit_report`.
+
+ :param modelpars: Parameters with "Known Values" (optional, default None)
+ :param show_correl: whether to show list of sorted correlations [``True``]
+ :param min_correl: smallest correlation absolute value to show [0.1]
+
+
+.. method:: ModelResult.conf_interval(**kwargs)
+
+ calculate the confidence intervals for the variable parameters using
+ :func:`confidence.conf_interval() <lmfit.conf_interval>`. All keyword
+ arguments are passed to that function. The result is stored in
+ :attr:`ci_out`, and so can be accessed without recalculating them.
+
+.. method:: ModelResult.ci_report(with_offset=True)
+
+ return a nicely formatted text report of the confidence intervals, as
+ from :func:`ci_report() <lmfit.ci_report>`.
+
+
+.. method:: ModelResult.plot(datafmt='o', fitfmt='-', initfmt='--', yerr=None, numpoints=None, fig=None, data_kws=None, fit_kws=None, init_kws=None, ax_res_kws=None, ax_fit_kws=None, fig_kws=None)
+
+ Plot the fit results and residuals using matplotlib, if available. The
+ plot will include two panels, one showing the fit residual, and the
+ other with the data points, the initial fit curve, and the best-fit
+ curve. If the fit model included weights or if ``yerr`` is specified,
+ errorbars will also be plotted.
+
+ :param datafmt: matplotlib format string for data curve.
+ :type datafmt: ``None`` or string.
+ :param fitfmt: matplotlib format string for best-fit curve.
+ :type fitfmt: ``None`` or string.
+ :param initfmt: matplotlib format string for initial curve.
+ :type intfmt: ``None`` or string.
+ :param yerr: array of uncertainties for data array.
+ :type yerr: ``None`` or ndarray.
+ :param numpoints: number of points to display
+ :type numpoints: ``None`` or integer
+ :param fig: matplotlib Figure to plot on.
+ :type fig: ``None`` or matplotlib.figure.Figure
+ :param data_kws: keyword arguments passed to plot for data curve.
+ :type data_kws: ``None`` or dictionary
+ :param fit_kws: keyword arguments passed to plot for best-fit curve.
+ :type fit_kws: ``None`` or dictionary
+ :param init_kws: keyword arguments passed to plot for initial curve.
+ :type init_kws: ``None`` or dictionary
+ :param ax_res_kws: keyword arguments passed to creation of matplotlib axes for the residual plot.
+ :type ax_res_kws: ``None`` or dictionary
+ :param ax_fit_kws: keyword arguments passed to creation of matplotlib axes for the fit plot.
+ :type ax_fit_kws: ``None`` or dictionary
+ :param fig_kws: keyword arguments passed to creation of matplotlib figure.
+ :type fig_kws: ``None`` or dictionary
+ :returns: matplotlib.figure.Figure
+
+ This combines :meth:`ModelResult.plot_fit` and :meth:`ModelResult.plot_residual`.
+
+ If ``yerr`` is specified or if the fit model included weights, then
+ matplotlib.axes.Axes.errorbar is used to plot the data. If ``yerr`` is
+ not specified and the fit includes weights, ``yerr`` set to ``1/self.weights``
+
+ If ``fig`` is None then ``matplotlib.pyplot.figure(**fig_kws)`` is called.
+
+.. method:: ModelResult.plot_fit(ax=None, datafmt='o', fitfmt='-', initfmt='--', yerr=None, numpoints=None, data_kws=None, fit_kws=None, init_kws=None, ax_kws=None)
+
+ Plot the fit results using matplotlib, if available. The plot will include
+ the data points, the initial fit curve, and the best-fit curve. If the fit
+ model included weights or if ``yerr`` is specified, errorbars will also
+ be plotted.
+
+ :param ax: matplotlib axes to plot on.
+ :type ax: ``None`` or matplotlib.axes.Axes.
+ :param datafmt: matplotlib format string for data curve.
+ :type datafmt: ``None`` or string.
+ :param fitfmt: matplotlib format string for best-fit curve.
+ :type fitfmt: ``None`` or string.
+ :param initfmt: matplotlib format string for initial curve.
+ :type intfmt: ``None`` or string.
+ :param yerr: array of uncertainties for data array.
+ :type yerr: ``None`` or ndarray.
+ :param numpoints: number of points to display
+ :type numpoints: ``None`` or integer
+ :param data_kws: keyword arguments passed to plot for data curve.
+ :type data_kws: ``None`` or dictionary
+ :param fit_kws: keyword arguments passed to plot for best-fit curve.
+ :type fit_kws: ``None`` or dictionary
+ :param init_kws: keyword arguments passed to plot for initial curve.
+ :type init_kws: ``None`` or dictionary
+ :param ax_kws: keyword arguments passed to creation of matplotlib axes.
+ :type ax_kws: ``None`` or dictionary
+ :returns: matplotlib.axes.Axes
+
+ For details about plot format strings and keyword arguments see
+ documentation of :func:`matplotlib.axes.Axes.plot`.
+
+ If ``yerr`` is specified or if the fit model included weights, then
+ matplotlib.axes.Axes.errorbar is used to plot the data. If ``yerr`` is
+ not specified and the fit includes weights, ``yerr`` set to ``1/self.weights``
+
+ If ``ax`` is None then ``matplotlib.pyplot.gca(**ax_kws)`` is called.
+
+.. method:: ModelResult.plot_residuals(ax=None, datafmt='o', yerr=None, data_kws=None, fit_kws=None, ax_kws=None)
+
+ Plot the fit residuals (data - fit) using matplotlib. If ``yerr`` is
+ supplied or if the model included weights, errorbars will also be plotted.
+
+ :param ax: matplotlib axes to plot on.
+ :type ax: ``None`` or matplotlib.axes.Axes.
+ :param datafmt: matplotlib format string for data curve.
+ :type datafmt: ``None`` or string.
+ :param yerr: array of uncertainties for data array.
+ :type yerr: ``None`` or ndarray.
+ :param numpoints: number of points to display
+ :type numpoints: ``None`` or integer
+ :param data_kws: keyword arguments passed to plot for data curve.
+ :type data_kws: ``None`` or dictionary
+ :param fit_kws: keyword arguments passed to plot for best-fit curve.
+ :type fit_kws: ``None`` or dictionary
+ :param ax_kws: keyword arguments passed to creation of matplotlib axes.
+ :type ax_kws: ``None`` or dictionary
+ :returns: matplotlib.axes.Axes
+
+ For details about plot format strings and keyword arguments see
+ documentation of :func:`matplotlib.axes.Axes.plot`.
+
+ If ``yerr`` is specified or if the fit model included weights, then
+ matplotlib.axes.Axes.errorbar is used to plot the data. If ``yerr`` is
+ not specified and the fit includes weights, ``yerr`` set to ``1/self.weights``
+
+ If ``ax`` is None then ``matplotlib.pyplot.gca(**ax_kws)`` is called.
+
+
+
+
+:class:`ModelResult` attributes
+---------------------------------
+
+.. attribute:: aic
+
+ floating point best-fit Akaike Information Criterion statistic (see :ref:`fit-results-label`).
+
+.. attribute:: best_fit
+
+ ndarray result of model function, evaluated at provided
+ independent variables and with best-fit parameters.
+
+.. attribute:: best_values
+
+ dictionary with parameter names as keys, and best-fit values as values.
+
+.. attribute:: bic
+
+ floating point best-fit Bayesian Information Criterion statistic (see :ref:`fit-results-label`).
+
+.. attribute:: chisqr
+
+ floating point best-fit chi-square statistic (see :ref:`fit-results-label`).
+
+.. attribute:: ci_out
+
+ confidence interval data (see :ref:`confidence_chapter`) or `None` if
+ the confidence intervals have not been calculated.
+
+.. attribute:: covar
+
+ ndarray (square) covariance matrix returned from fit.
+
+.. attribute:: data
+
+ ndarray of data to compare to model.
+
+.. attribute:: errorbars
+
+ boolean for whether error bars were estimated by fit.
+
+.. attribute:: ier
+
+ integer returned code from :scipydoc:`optimize.leastsq`.
+
+.. attribute:: init_fit
+
+ ndarray result of model function, evaluated at provided
+ independent variables and with initial parameters.
+
+.. attribute:: init_params
+
+ initial parameters.
+
+.. attribute:: init_values
+
+ dictionary with parameter names as keys, and initial values as values.
+
+.. attribute:: iter_cb
+
+ optional callable function, to be called at each fit iteration. This
+ must take take arguments of ``params, iter, resid, *args, **kws``, where
+ ``params`` will have the current parameter values, ``iter`` the
+ iteration, ``resid`` the current residual array, and ``*args`` and
+ ``**kws`` as passed to the objective function. See :ref:`fit-itercb-label`.
+
+.. attribute:: jacfcn
+
+ optional callable function, to be called to calculate jacobian array.
+
+.. attribute:: lmdif_message
+
+ string message returned from :scipydoc:`optimize.leastsq`.
+
+.. attribute:: message
+
+ string message returned from :func:`minimize`.
+
+.. attribute:: method
+
+ string naming fitting method for :func:`minimize`.
+
+.. attribute:: model
+
+ instance of :class:`Model` used for model.
+
+.. attribute:: ndata
+
+ integer number of data points.
+
+.. attribute:: nfev
+
+ integer number of function evaluations used for fit.
+
+.. attribute:: nfree
+
+ integer number of free parameters in fit.
+
+.. attribute:: nvarys
+
+ integer number of independent, freely varying variables in fit.
+
+.. attribute:: params
+
+ Parameters used in fit. Will have best-fit values.
+
+.. attribute:: redchi
+
+ floating point reduced chi-square statistic (see :ref:`fit-results-label`).
+
+.. attribute:: residual
+
+ ndarray for residual.
+
+.. attribute:: scale_covar
+
+ boolean flag for whether to automatically scale covariance matrix.
+
+.. attribute:: success
+
+ boolean value of whether fit succeeded.
+
+.. attribute:: weights
+
+ ndarray (or ``None``) of weighting values to be used in fit. If not
+ ``None``, it will be used as a multiplicative factor of the residual
+ array, so that ``weights*(data - fit)`` is minimized in the
+ least-squares sense.
+
+.. index:: Composite models
+
+.. _composite_models_section:
+
+
+Composite Models : adding (or multiplying) Models
+==============================================================
+
+One of the more interesting features of the :class:`Model` class is that
+Models can be added together or combined with basic algebraic operations
+(add, subtract, multiply, and divide) to give a composite model. The
+composite model will have parameters from each of the component models,
+with all parameters being available to influence the whole model. This
+ability to combine models will become even more useful in the next chapter,
+when pre-built subclasses of :class:`Model` are discussed. For now, we'll
+consider a simple example, and build a model of a Gaussian plus a line, as
+to model a peak with a background. For such a simple problem, we could just
+build a model that included both components::
+
+ def gaussian_plus_line(x, amp, cen, wid, slope, intercept):
+ "line + 1-d gaussian"
+
+ gauss = (amp/(sqrt(2*pi)*wid)) * exp(-(x-cen)**2 /(2*wid**2))
+ line = slope * x + intercept
+ return gauss + line
+
+and use that with::
+
+ mod = Model(gaussian_plus_line)
+
+But we already had a function for a gaussian function, and maybe we'll
+discover that a linear background isn't sufficient which would mean the
+model function would have to be changed. As an alternative we could define
+a linear function::
+
+ def line(x, slope, intercept):
+ "a line"
+ return slope * x + intercept
+
+and build a composite model with just::
+
+ mod = Model(gaussian) + Model(line)
+
+This model has parameters for both component models, and can be used as:
+
+.. literalinclude:: ../examples/doc_model2.py
+
+which prints out the results::
+
+ [[Model]]
+ (Model(gaussian) + Model(line))
+ [[Fit Statistics]]
+ # function evals = 44
+ # data points = 101
+ # variables = 5
+ chi-square = 2.579
+ reduced chi-square = 0.027
+ Akaike info crit = -355.329
+ Bayesian info crit = -342.253
+ [[Variables]]
+ amp: 8.45931061 +/- 0.124145 (1.47%) (init= 5)
+ cen: 5.65547872 +/- 0.009176 (0.16%) (init= 5)
+ intercept: -0.96860201 +/- 0.033522 (3.46%) (init= 1)
+ slope: 0.26484403 +/- 0.005748 (2.17%) (init= 0)
+ wid: 0.67545523 +/- 0.009916 (1.47%) (init= 1)
+ [[Correlations]] (unreported correlations are < 0.100)
+ C(amp, wid) = 0.666
+ C(cen, intercept) = 0.129
+
+
+and shows the plot on the left.
+
+.. _figModel2:
+
+ .. image:: _images/model_fit2.png
+ :target: _images/model_fit2.png
+ :width: 48%
+ .. image:: _images/model_fit2a.png
+ :target: _images/model_fit2a.png
+ :width: 48%
+
+
+On the left, data is shown in blue dots, the total fit is shown in solid
+red line, and the initial fit is shown as a black dashed line. In the
+figure on the right, the data is again shown in blue dots, and the Gaussian
+component shown as a black dashed line, and the linear component shown as a
+red dashed line. These components were generated after the fit using the
+Models :meth:`ModelResult.eval_components` method of the `result`::
+
+ comps = result.eval_components()
+
+which returns a dictionary of the components, using keys of the model name
+(or `prefix` if that is set). This will use the parameter values in
+``result.params`` and the independent variables (``x``) used during the
+fit. Note that while the :class:`ModelResult` held in `result` does store the
+best parameters and the best estimate of the model in ``result.best_fit``,
+the original model and parameters in ``pars`` are left unaltered.
+
+You can apply this composite model to other data sets, or evaluate the
+model at other values of ``x``. You may want to do this to give a finer or
+coarser spacing of data point, or to extrapolate the model outside the
+fitting range. This can be done with::
+
+ xwide = np.linspace(-5, 25, 3001)
+ predicted = mod.eval(x=xwide)
+
+In this example, the argument names for the model functions do not overlap.
+If they had, the ``prefix`` argument to :class:`Model` would have allowed
+us to identify which parameter went with which component model. As we will
+see in the next chapter, using composite models with the built-in models
+provides a simple way to build up complex models.
+
+.. class:: CompositeModel(left, right, op[, **kws])
+
+ Create a composite model from two models (`left` and `right` and an
+ binary operator (`op`). Additional keywords are passed to
+ :class:`Model`.
+
+ :param left: left-hand side Model
+ :type left: :class:`Model`
+ :param right: right-hand side Model
+ :type right: :class:`Model`
+ :param op: binary operator
+ :type op: callable, and taking 2 arguments (`left` and `right`).
+
+Normally, one does not have to explicitly create a :class:`CompositeModel`,
+as doing::
+
+ mod = Model(fcn1) + Model(fcn2) * Model(fcn3)
+
+will automatically create a :class:`CompositeModel`. In this example,
+`mod.left` will be `Model(fcn1)`, `mod.op` will be :meth:`operator.add`,
+and `mod.right` will be another CompositeModel that has a `left` attribute
+of `Model(fcn2)`, an `op` of :meth:`operator.mul`, and a `right` of
+`Model(fcn3)`.
+
+If you want to use a binary operator other than add, subtract, multiply, or
+divide that are supported through normal Python syntax, you'll need to
+explicitly create a :class:`CompositeModel` with the appropriate binary
+operator. For example, to convolve two models, you could define a simple
+convolution function, perhaps as::
+
+ import numpy as np
+ def convolve(dat, kernel):
+ # simple convolution
+ npts = min(len(dat), len(kernel))
+ pad = np.ones(npts)
+ tmp = np.concatenate((pad*dat[0], dat, pad*dat[-1]))
+ out = np.convolve(tmp, kernel, mode='valid')
+ noff = int((len(out) - npts)/2)
+ return (out[noff:])[:npts]
+
+which extends the data in both directions so that the convolving kernel
+function gives a valid result over the data range. Because this function
+takes two array arguments and returns an array, it can be used as the
+binary operator. A full script using this technique is here:
+
+.. literalinclude:: ../examples/doc_model3.py
+
+which prints out the results::
+
+ [[Model]]
+ (Model(jump) <function convolve at 0x109ee4488> Model(gaussian))
+ [[Fit Statistics]]
+ # function evals = 23
+ # data points = 201
+ # variables = 3
+ chi-square = 25.789
+ reduced chi-square = 0.130
+ Akaike info crit = -403.702
+ Bayesian info crit = -393.793
+ [[Variables]]
+ mid: 5 (fixed)
+ amplitude: 0.62249894 +/- 0.001946 (0.31%) (init= 1)
+ sigma: 0.61438887 +/- 0.014057 (2.29%) (init= 1.5)
+ center: 4.51710256 +/- 0.010152 (0.22%) (init= 3.5)
+ [[Correlations]] (unreported correlations are < 0.100)
+ C(amplitude, center) = 0.335
+ C(amplitude, sigma) = 0.273
+
+and shows the plots:
+
+.. _figModel3:
+
+ .. image:: _images/model_fit3a.png
+ :target: _images/model_fit3a.png
+ :width: 48%
+ .. image:: _images/model_fit3b.png
+ :target: _images/model_fit3b.png
+ :width: 48%
+
+Using composite models with built-in or custom operators allows you to
+build complex models from testable sub-components.
diff --git a/doc/parameters.rst b/doc/parameters.rst
index 980d809..e9b53d7 100644
--- a/doc/parameters.rst
+++ b/doc/parameters.rst
@@ -1,240 +1,237 @@
-.. _parameters_chapter:
-
-================================================
-:class:`Parameter` and :class:`Parameters`
-================================================
-
-This chapter describes :class:`Parameter` objects which is the key concept
-of lmfit.
-
-A :class:`Parameter` is the quantity to be optimized in all minimization
-problems, replacing the plain floating point number used in the
-optimization routines from :mod:`scipy.optimize`. A :class:`Parameter` has
-a value that can be varied in the fit or have a fixed value, have upper
-and/or lower bounds. It can even have a value that is constrained by an
-algebraic expression of other Parameter values. Since :class:`Parameters`
-live outside the core optimization routines, they can be used in **all**
-optimization routines from :mod:`scipy.optimize`. By using
-:class:`Parameter` objects instead of plain variables, the objective
-function does not have to be modified to reflect every change of what is
-varied in the fit. This simplifies the writing of models, allowing general
-models that describe the phenomenon to be written, and gives the user more
-flexibility in using and testing variations of that model.
-
-Whereas a :class:`Parameter` expands on an individual floating point
-variable, the optimization methods need an ordered group of floating point
-variables. In the :mod:`scipy.optimize` routines this is required to be a
-1-dimensional numpy ndarray. For lmfit, where each :class:`Parameter` has
-a name, this is replaced by a :class:`Parameters` class, which works as an
-ordered dictionary of :class:`Parameter` objects, with a few additional
-features and methods. That is, while the concept of a :class:`Parameter`
-is central to lmfit, one normally creates and interacts with a
-:class:`Parameters` instance that contains many :class:`Parameter` objects.
-The objective functions you write for lmfit will take an instance of
-:class:`Parameters` as its first argument.
-
-
-The :class:`Parameter` class
-========================================
-
-.. class:: Parameter(name=None[, value=None[, vary=True[, min=None[, max=None[, expr=None]]]]])
-
- create a Parameter object.
-
- :param name: parameter name
- :type name: ``None`` or string -- will be overwritten during fit if ``None``.
- :param value: the numerical value for the parameter
- :param vary: whether to vary the parameter or not.
- :type vary: boolean (``True``/``False``) [default ``True``]
- :param min: lower bound for value (``None`` = no lower bound).
- :param max: upper bound for value (``None`` = no upper bound).
- :param expr: mathematical expression to use to evaluate value during fit.
- :type expr: ``None`` or string
-
-
-Each of these inputs is turned into an attribute of the same name.
-
-After a fit, a Parameter for a fitted variable (that is with ``vary =
-True``) may have its :attr:`value` attribute to hold the best-fit value.
-Depending on the success of the fit and fitting algorithm used, it may also
-have attributes :attr:`stderr` and :attr:`correl`.
-
-.. attribute:: stderr
-
- the estimated standard error for the best-fit value.
-
-.. attribute:: correl
-
- a dictionary of the correlation with the other fitted variables in the
- fit, of the form::
-
- {'decay': 0.404, 'phase': -0.020, 'frequency': 0.102}
-
-See :ref:`bounds_chapter` for details on the math used to implement the
-bounds with :attr:`min` and :attr:`max`.
-
-The :attr:`expr` attribute can contain a mathematical expression that will
-be used to compute the value for the Parameter at each step in the fit.
-See :ref:`constraints_chapter` for more details and examples of this
-feature.
-
-.. index:: Removing a Constraint Expression
-
-.. method:: set(value=None[, vary=None[, min=None[, max=None[, expr=None]]]])
-
- set or update a Parameters value or other attributes.
-
- :param name: parameter name
- :param value: the numerical value for the parameter
- :param vary: whether to vary the parameter or not.
- :param min: lower bound for value
- :param max: upper bound for value
- :param expr: mathematical expression to use to evaluate value during fit.
-
-Each argument of :meth:`set` has a default value of ``None``, and will
-be set only if the provided value is not ``None``. You can use this to
-update some Parameter attribute without affecting others, for example::
-
- p1 = Parameter('a', value=2.0)
- p2 = Parameter('b', value=0.0)
- p1.set(min=0)
- p2.set(vary=False)
-
- to set a lower bound, or to set a Parameter as have a fixed value.
-
- Note that to use this approach to lift a lower or upper bound, doing::
-
- p1.set(min=0)
- .....
- # now lift the lower bound
- p1.set(min=None) # won't work! lower bound NOT changed
-
- won't work -- this will not change the current lower bound. Instead
- you'll have to use ``np.inf`` to remove a lower or upper bound::
-
- # now lift the lower bound
- p1.set(min=-np.inf) # will work!
-
- Similarly, to clear an expression of a parameter, you need to pass an
- empty string, not ``None``. You also need to give a value and
- explicitly tell it to vary::
-
- p3 = Parameter('c', expr='(a+b)/2')
- p3.set(expr=None) # won't work! expression NOT changed
-
- # remove constraint expression
- p3.set(value=1.0, vary=True, expr='') # will work! parameter now unconstrained
-
-
-The :class:`Parameters` class
-========================================
-
-.. class:: Parameters()
-
- create a Parameters object. This is little more than a fancy ordered
- dictionary, with the restrictions that:
-
- 1. keys must be valid Python symbol names, so that they can be used in
- expressions of mathematical constraints. This means the names must
- match ``[a-z_][a-z0-9_]*`` and cannot be a Python reserved word.
-
- 2. values must be valid :class:`Parameter` objects.
-
-
- Two methods are for provided for convenient initialization of a :class:`Parameters`,
- and one for extracting :class:`Parameter` values into a plain dictionary.
-
-.. method:: add(name[, value=None[, vary=True[, min=None[, max=None[, expr=None]]]]])
-
- add a named parameter. This creates a :class:`Parameter`
- object associated with the key `name`, with optional arguments
- passed to :class:`Parameter`::
-
- p = Parameters()
- p.add('myvar', value=1, vary=True)
-
-.. method:: add_many(self, paramlist)
-
- add a list of named parameters. Each entry must be a tuple
- with the following entries::
-
- name, value, vary, min, max, expr
-
- This method is somewhat rigid and verbose (no default values), but can
- be useful when initially defining a parameter list so that it looks
- table-like::
-
- p = Parameters()
- # (Name, Value, Vary, Min, Max, Expr)
- p.add_many(('amp1', 10, True, None, None, None),
- ('cen1', 1.2, True, 0.5, 2.0, None),
- ('wid1', 0.8, True, 0.1, None, None),
- ('amp2', 7.5, True, None, None, None),
- ('cen2', 1.9, True, 1.0, 3.0, None),
- ('wid2', None, False, None, None, '2*wid1/3'))
-
-
-.. method:: pretty_print(oneline=False)
-
- prints a clean representation on the Parameters. If `oneline` is
- `True`, the result will be printed to a single (long) line.
-
-.. method:: valuesdict()
-
- return an ordered dictionary of name:value pairs with the
- Paramater name as the key and Parameter value as value.
-
- This is distinct from the :class:`Parameters` itself, as the dictionary
- values are not :class:`Parameter` objects, just the :attr:`value`.
- Using :method:`valuesdict` can be a very convenient way to get updated
- values in a objective function.
-
-.. method:: dumps(**kws):
-
- return a JSON string representation of the :class:`Parameter` object.
- This can be saved or used to re-create or re-set parameters, using the
- :meth:`loads` method.
-
- Optional keywords are sent :py:func:`json.dumps`.
-
-.. method:: dump(file, **kws):
-
- write a JSON representation of the :class:`Parameter` object to a file
- or file-like object in `file` -- really any object with a :meth:`write`
- method. Optional keywords are sent :py:func:`json.dumps`.
-
-.. method:: loads(sval, **kws):
-
- use a JSON string representation of the :class:`Parameter` object in
- `sval` to set all parameter settins. Optional keywords are sent
- :py:func:`json.loads`.
-
-.. method:: load(file, **kws):
-
- read and use a JSON string representation of the :class:`Parameter`
- object from a file or file-like object in `file` -- really any object
- with a :meth:`read` method. Optional keywords are sent
- :py:func:`json.loads`.
-
-
-Simple Example
-==================
-
-Using :class:`Parameters`` and :func:`minimize` function (discussed in the
-next chapter) might look like this:
-
-.. literalinclude:: ../examples/doc_basic.py
-
-
-Here, the objective function explicitly unpacks each Parameter value. This
-can be simplified using the :class:`Parameters` :meth:`valuesdict` method,
-which would make the objective function ``fcn2min`` above look like::
-
- def fcn2min(params, x, data):
- """ model decaying sine wave, subtract data"""
- v = params.valuesdict()
-
- model = v['amp'] * np.sin(x * v['omega'] + v['shift']) * np.exp(-x*x*v['decay'])
- return model - data
-
-The results are identical, and the difference is a stylistic choice.
+.. _parameters_chapter:
+
+================================================
+:class:`Parameter` and :class:`Parameters`
+================================================
+
+This chapter describes :class:`Parameter` objects which is the key concept
+of lmfit.
+
+A :class:`Parameter` is the quantity to be optimized in all minimization
+problems, replacing the plain floating point number used in the
+optimization routines from :mod:`scipy.optimize`. A :class:`Parameter` has
+a value that can be varied in the fit or have a fixed value, have upper
+and/or lower bounds. It can even have a value that is constrained by an
+algebraic expression of other Parameter values. Since :class:`Parameters`
+live outside the core optimization routines, they can be used in **all**
+optimization routines from :mod:`scipy.optimize`. By using
+:class:`Parameter` objects instead of plain variables, the objective
+function does not have to be modified to reflect every change of what is
+varied in the fit. This simplifies the writing of models, allowing general
+models that describe the phenomenon to be written, and gives the user more
+flexibility in using and testing variations of that model.
+
+Whereas a :class:`Parameter` expands on an individual floating point
+variable, the optimization methods need an ordered group of floating point
+variables. In the :mod:`scipy.optimize` routines this is required to be a
+1-dimensional numpy ndarray. For lmfit, where each :class:`Parameter` has
+a name, this is replaced by a :class:`Parameters` class, which works as an
+ordered dictionary of :class:`Parameter` objects, with a few additional
+features and methods. That is, while the concept of a :class:`Parameter`
+is central to lmfit, one normally creates and interacts with a
+:class:`Parameters` instance that contains many :class:`Parameter` objects.
+The objective functions you write for lmfit will take an instance of
+:class:`Parameters` as its first argument.
+
+
+The :class:`Parameter` class
+========================================
+
+.. class:: Parameter(name=None[, value=None[, vary=True[, min=None[, max=None[, expr=None]]]]])
+
+ create a Parameter object.
+
+ :param name: parameter name
+ :type name: ``None`` or string -- will be overwritten during fit if ``None``.
+ :param value: the numerical value for the parameter
+ :param vary: whether to vary the parameter or not.
+ :type vary: boolean (``True``/``False``) [default ``True``]
+ :param min: lower bound for value (``None`` = no lower bound).
+ :param max: upper bound for value (``None`` = no upper bound).
+ :param expr: mathematical expression to use to evaluate value during fit.
+ :type expr: ``None`` or string
+
+ Each of these inputs is turned into an attribute of the same name.
+
+ After a fit, a Parameter for a fitted variable (that is with ``vary =
+ True``) may have its :attr:`value` attribute to hold the best-fit value.
+ Depending on the success of the fit and fitting algorithm used, it may also
+ have attributes :attr:`stderr` and :attr:`correl`.
+
+ .. attribute:: stderr
+
+ the estimated standard error for the best-fit value.
+
+ .. attribute:: correl
+
+ a dictionary of the correlation with the other fitted variables in the
+ fit, of the form::
+
+ {'decay': 0.404, 'phase': -0.020, 'frequency': 0.102}
+
+ See :ref:`bounds_chapter` for details on the math used to implement the
+ bounds with :attr:`min` and :attr:`max`.
+
+ The :attr:`expr` attribute can contain a mathematical expression that will
+ be used to compute the value for the Parameter at each step in the fit.
+ See :ref:`constraints_chapter` for more details and examples of this
+ feature.
+
+ .. index:: Removing a Constraint Expression
+
+ .. method:: set(value=None[, vary=None[, min=None[, max=None[, expr=None]]]])
+
+ set or update a Parameters value or other attributes.
+
+ :param name: parameter name
+ :param value: the numerical value for the parameter
+ :param vary: whether to vary the parameter or not.
+ :param min: lower bound for value
+ :param max: upper bound for value
+ :param expr: mathematical expression to use to evaluate value during fit.
+
+ Each argument of :meth:`set` has a default value of ``None``, and will
+ be set only if the provided value is not ``None``. You can use this to
+ update some Parameter attribute without affecting others, for example::
+
+ p1 = Parameter('a', value=2.0)
+ p2 = Parameter('b', value=0.0)
+ p1.set(min=0)
+ p2.set(vary=False)
+
+ to set a lower bound, or to set a Parameter as have a fixed value.
+
+ Note that to use this approach to lift a lower or upper bound, doing::
+
+ p1.set(min=0)
+ .....
+ # now lift the lower bound
+ p1.set(min=None) # won't work! lower bound NOT changed
+
+ won't work -- this will not change the current lower bound. Instead
+ you'll have to use ``np.inf`` to remove a lower or upper bound::
+
+ # now lift the lower bound
+ p1.set(min=-np.inf) # will work!
+
+ Similarly, to clear an expression of a parameter, you need to pass an
+ empty string, not ``None``. You also need to give a value and
+ explicitly tell it to vary::
+
+ p3 = Parameter('c', expr='(a+b)/2')
+ p3.set(expr=None) # won't work! expression NOT changed
+
+ # remove constraint expression
+ p3.set(value=1.0, vary=True, expr='') # will work! parameter now unconstrained
+
+
+The :class:`Parameters` class
+========================================
+
+.. currentmodule:: lmfit.parameter
+
+.. class:: Parameters()
+
+ create a Parameters object. This is little more than a fancy ordered
+ dictionary, with the restrictions that:
+
+ 1. keys must be valid Python symbol names, so that they can be used in
+ expressions of mathematical constraints. This means the names must
+ match ``[a-z_][a-z0-9_]*`` and cannot be a Python reserved word.
+
+ 2. values must be valid :class:`Parameter` objects.
+
+ Two methods are provided for convenient initialization of a :class:`Parameters`,
+ and one for extracting :class:`Parameter` values into a plain dictionary.
+
+ .. method:: add(name[, value=None[, vary=True[, min=None[, max=None[, expr=None]]]]])
+
+ add a named parameter. This creates a :class:`Parameter`
+ object associated with the key `name`, with optional arguments
+ passed to :class:`Parameter`::
+
+ p = Parameters()
+ p.add('myvar', value=1, vary=True)
+
+ .. method:: add_many(self, paramlist)
+
+ add a list of named parameters. Each entry must be a tuple
+ with the following entries::
+
+ name, value, vary, min, max, expr
+
+ This method is somewhat rigid and verbose (no default values), but can
+ be useful when initially defining a parameter list so that it looks
+ table-like::
+
+ p = Parameters()
+ # (Name, Value, Vary, Min, Max, Expr)
+ p.add_many(('amp1', 10, True, None, None, None),
+ ('cen1', 1.2, True, 0.5, 2.0, None),
+ ('wid1', 0.8, True, 0.1, None, None),
+ ('amp2', 7.5, True, None, None, None),
+ ('cen2', 1.9, True, 1.0, 3.0, None),
+ ('wid2', None, False, None, None, '2*wid1/3'))
+
+
+ .. automethod:: Parameters.pretty_print
+
+ .. method:: valuesdict()
+
+ return an ordered dictionary of name:value pairs with the
+ Paramater name as the key and Parameter value as value.
+
+ This is distinct from the :class:`Parameters` itself, as the dictionary
+ values are not :class:`Parameter` objects, just the :attr:`value`.
+ Using :meth:`valuesdict` can be a very convenient way to get updated
+ values in a objective function.
+
+ .. method:: dumps(**kws)
+
+ return a JSON string representation of the :class:`Parameter` object.
+ This can be saved or used to re-create or re-set parameters, using the
+ :meth:`loads` method.
+
+ Optional keywords are sent :py:func:`json.dumps`.
+
+ .. method:: dump(file, **kws)
+
+ write a JSON representation of the :class:`Parameter` object to a file
+ or file-like object in `file` -- really any object with a :meth:`write`
+ method. Optional keywords are sent :py:func:`json.dumps`.
+
+ .. method:: loads(sval, **kws)
+
+ use a JSON string representation of the :class:`Parameter` object in
+ `sval` to set all parameter settings. Optional keywords are sent
+ :py:func:`json.loads`.
+
+ .. method:: load(file, **kws)
+
+ read and use a JSON string representation of the :class:`Parameter`
+ object from a file or file-like object in `file` -- really any object
+ with a :meth:`read` method. Optional keywords are sent
+ :py:func:`json.loads`.
+
+
+Simple Example
+==================
+
+Using :class:`Parameters`` and :func:`minimize` function (discussed in the
+next chapter) might look like this:
+
+.. literalinclude:: ../examples/doc_basic.py
+
+
+Here, the objective function explicitly unpacks each Parameter value. This
+can be simplified using the :class:`Parameters` :meth:`valuesdict` method,
+which would make the objective function ``fcn2min`` above look like::
+
+ def fcn2min(params, x, data):
+ """ model decaying sine wave, subtract data"""
+ v = params.valuesdict()
+
+ model = v['amp'] * np.sin(x * v['omega'] + v['shift']) * np.exp(-x*x*v['decay'])
+ return model - data
+
+The results are identical, and the difference is a stylistic choice.
diff --git a/doc/sphinx/ext_mathjax.py b/doc/sphinx/ext_mathjax.py
index 3e54c82..40de659 100644
--- a/doc/sphinx/ext_mathjax.py
+++ b/doc/sphinx/ext_mathjax.py
@@ -1,10 +1,10 @@
-# sphinx extensions for mathjax
-extensions = ['sphinx.ext.autodoc',
- 'sphinx.ext.todo',
- 'sphinx.ext.coverage',
- 'sphinx.ext.intersphinx',
- 'numpydoc']
-mathjax = 'sphinx.ext.mathjax'
-pngmath = 'sphinx.ext.pngmath'
-
-extensions.append(mathjax)
+# sphinx extensions for mathjax
+extensions = ['sphinx.ext.autodoc',
+ 'sphinx.ext.todo',
+ 'sphinx.ext.coverage',
+ 'sphinx.ext.intersphinx',
+ 'numpydoc']
+mathjax = 'sphinx.ext.mathjax'
+pngmath = 'sphinx.ext.pngmath'
+
+extensions.append(mathjax)
diff --git a/doc/sphinx/ext_pngmath.py b/doc/sphinx/ext_pngmath.py
index 10997b0..cf153fe 100644
--- a/doc/sphinx/ext_pngmath.py
+++ b/doc/sphinx/ext_pngmath.py
@@ -1,10 +1,10 @@
-# sphinx extensions for pngmath
-extensions = ['sphinx.ext.autodoc',
- 'sphinx.ext.todo',
- 'sphinx.ext.coverage',
- 'sphinx.ext.intersphinx',
- 'numpydoc']
-mathjax = 'sphinx.ext.mathjax'
-pngmath = 'sphinx.ext.pngmath'
-
-extensions.append(pngmath)
+# sphinx extensions for pngmath
+extensions = ['sphinx.ext.autodoc',
+ 'sphinx.ext.todo',
+ 'sphinx.ext.coverage',
+ 'sphinx.ext.intersphinx',
+ 'numpydoc']
+mathjax = 'sphinx.ext.mathjax'
+pngmath = 'sphinx.ext.pngmath'
+
+extensions.append(pngmath)
diff --git a/doc/sphinx/theme/lmfitdoc/layout.html b/doc/sphinx/theme/lmfitdoc/layout.html
index 42409a1..6a31b9d 100644
--- a/doc/sphinx/theme/lmfitdoc/layout.html
+++ b/doc/sphinx/theme/lmfitdoc/layout.html
@@ -1,66 +1,66 @@
-{#
- sphinxdoc/layout.html
- ~~~~~~~~~~~~~~~~~~~~~
-
- Sphinx layout template for the sphinxdoc theme.
-
- :copyright: Copyright 2007-2014 by the Sphinx team, see AUTHORS.
- :license: BSD, see LICENSE for details.
-#}
-{%- extends "basic/layout.html" %}
-
-{%- block extrahead %}
- <script type="text/x-mathjax-config">
- MathJax.Hub.Config({
- "TeX": {Macros: {AA : "{\\unicode{x212B}}"}},
- "HTML-CSS": {scale: 90}
- });</script>
-{% endblock %}
-
-
-
-{% block rootrellink %}
- <li>[<a href="{{ pathto('intro') }}">intro</a>|</li>
- <li><a href="{{ pathto('parameters') }}">parameters</a>|</li>
- <li><a href="{{ pathto('fitting') }}"> minimize</a>|</li>
- <li><a href="{{ pathto('model') }}"> model</a>|</li>
- <li><a href="{{ pathto('builtin_models') }}"> builtin models</a>|</li>
- <li><a href="{{ pathto('confidence') }}">confidence intervals</a>|</li>
- <li><a href="{{ pathto('bounds') }}">bounds</a>|</li>
- <li><a href="{{ pathto('constraints') }}">constraints</a>]</li>
-{% endblock %}
-
-{% block relbar1 %}
-<div>
-<table border=0>
- <tr><td></td><td width=85% padding=5 align=left>
- <a href="index.html" style="color: #157"> <font size=+3>LMFIT</font></a>
- </td>
- <td width=7% align=left>
- <a href="contents.html" style="color: #882222">
- <font size+=1>Contents</font></a> </td>
- <td width=7% align=left>
- <a href="installation.html" style="color: #882222">
- <font size+=1>Download</font></a></td>
- <td></td>
- </tr>
- <tr><td></td><td width=75% padding=5 align=left>
- <a href="index.html" style="color: #157"> <font size=+2>
- Non-Linear Least-Squares Minimization and Curve-Fitting for Python</font></a>
- </td>
- <td width=7% align=left>
- <a href="faq.html" style="color: #882222">
- <font size+=1>FAQ</font></a> </td>
- <td width=7% align=left>
- <a href="https://github.com/lmfit/lmfit-py/" style="color: #882222">
- <font size+=1>Develop</font></a></td>
- <td></td>
- </tr>
-</table>
-</div>
-{{ super() }}
-{% endblock %}
-
-{# put the sidebar before the body #}
-{% block sidebar1 %}{{ sidebar() }}{% endblock %}
-{% block sidebar2 %}{% endblock %}
+{#
+ sphinxdoc/layout.html
+ ~~~~~~~~~~~~~~~~~~~~~
+
+ Sphinx layout template for the sphinxdoc theme.
+
+ :copyright: Copyright 2007-2014 by the Sphinx team, see AUTHORS.
+ :license: BSD, see LICENSE for details.
+#}
+{%- extends "basic/layout.html" %}
+
+{%- block extrahead %}
+ <script type="text/x-mathjax-config">
+ MathJax.Hub.Config({
+ "TeX": {Macros: {AA : "{\\unicode{x212B}}"}},
+ "HTML-CSS": {scale: 90}
+ });</script>
+{% endblock %}
+
+
+
+{% block rootrellink %}
+ <li>[<a href="{{ pathto('intro') }}">intro</a>|</li>
+ <li><a href="{{ pathto('parameters') }}">parameters</a>|</li>
+ <li><a href="{{ pathto('fitting') }}"> minimize</a>|</li>
+ <li><a href="{{ pathto('model') }}"> model</a>|</li>
+ <li><a href="{{ pathto('builtin_models') }}"> builtin models</a>|</li>
+ <li><a href="{{ pathto('confidence') }}">confidence intervals</a>|</li>
+ <li><a href="{{ pathto('bounds') }}">bounds</a>|</li>
+ <li><a href="{{ pathto('constraints') }}">constraints</a>]</li>
+{% endblock %}
+
+{% block relbar1 %}
+<div>
+<table border=0>
+ <tr><td></td><td width=85% padding=5 align=left>
+ <a href="index.html" style="color: #157"> <font size=+3>LMFIT</font></a>
+ </td>
+ <td width=7% align=left>
+ <a href="contents.html" style="color: #882222">
+ <font size+=1>Contents</font></a> </td>
+ <td width=7% align=left>
+ <a href="installation.html" style="color: #882222">
+ <font size+=1>Download</font></a></td>
+ <td></td>
+ </tr>
+ <tr><td></td><td width=75% padding=5 align=left>
+ <a href="index.html" style="color: #157"> <font size=+2>
+ Non-Linear Least-Squares Minimization and Curve-Fitting for Python</font></a>
+ </td>
+ <td width=7% align=left>
+ <a href="faq.html" style="color: #882222">
+ <font size+=1>FAQ</font></a> </td>
+ <td width=7% align=left>
+ <a href="https://github.com/lmfit/lmfit-py/" style="color: #882222">
+ <font size+=1>Develop</font></a></td>
+ <td></td>
+ </tr>
+</table>
+</div>
+{{ super() }}
+{% endblock %}
+
+{# put the sidebar before the body #}
+{% block sidebar1 %}{{ sidebar() }}{% endblock %}
+{% block sidebar2 %}{% endblock %}
diff --git a/doc/sphinx/theme/lmfitdoc/static/lmfitdoc.css_t b/doc/sphinx/theme/lmfitdoc/static/lmfitdoc.css_t
index 89bd30c..92b6913 100644
--- a/doc/sphinx/theme/lmfitdoc/static/lmfitdoc.css_t
+++ b/doc/sphinx/theme/lmfitdoc/static/lmfitdoc.css_t
@@ -1,348 +1,348 @@
-/*
- * lmfitdoc.css_t
- * minor riff on sphinxdoc.css_t
- * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
- *
- * Sphinx stylesheet -- sphinxdoc theme. Originally created by
- * Armin Ronacher for Werkzeug.
- *
- * :copyright: Copyright 2007-2014 by the Sphinx team, see AUTHORS.
- * :license: BSD, see LICENSE for details.
- *
- */
-
- at import url("basic.css");
-
-/* -- page layout ----------------------------------------------------------- */
-
-body {
- font-family: 'Lucida Grande', 'Lucida Sans Unicode', 'Geneva', 'Verdana', sans-serif;
- font-size: 14px;
- letter-spacing: -0.01em;
- line-height: 150%;
- text-align: center;
- background-color: #D6DAC4;
- color: black;
- padding: 0;
- border: 0px solid #D0D0C0;
- margin: 15px 15px 15px 15px;
- min-width: 740px;
-}
-
-div.document {
- background-color: white;
- text-align: left;
- background-image: url(contents.png);
- background-repeat: repeat-x;
-}
-
-div.bodywrapper {
- margin: 0 {{ theme_sidebarwidth|toint + 10 }}px 0 0;
- border-right: 1px solid #ccc;
-}
-
-div.body {
- margin: 0;
- padding: 0.5em 20px 20px 20px;
-}
-
-div.related {
- font-size: 1em;
- background-color: #0D0;
-}
-
-div.related ul {
- height: 2em;
- border-top: 1px solid #ddd;
- border-bottom: 1px solid #ddd;
- background-color: #F0EFE4;
- color: #157;
-}
-
-div.related ul li {
- margin: 0;
- padding: 0;
- height: 2em;
- float: left;
- background-color: #D0000;
-}
-
-div.related ul li.right {
- float: right;
- margin-right: 5px;
-}
-
-div.related ul li a {
- margin: 0;
- padding: 0 5px 0 5px;
- line-height: 1.75em;
- color: #EE9816;
- color: #157;
-}
-
-div.related ul li a:hover {
- color: #822;
-}
-
-div.sphinxsidebarwrapper {
- padding: 0;
-}
-
-div.sphinxsidebar {
- margin: 0;
- padding: 0.5em 15px 15px 0;
- width: {{ theme_sidebarwidth|toint - 20 }}px;
- float: right;
- font-size: 1em;
- text-align: left;
-}
-
-div.sphinxsidebar h3, div.sphinxsidebar h4 {
- margin: 1em 0 0.5em 0;
- font-size: 1em;
- padding: 0.1em 0 0.1em 0.5em;
- color: #157;
- border: 1px solid #A0A090;
- background-color: #D0D0C4;
-}
-
-div.sphinxsidebar h3 a {
- color: #157;
- background-color: #D0D0C4;
-}
-
-div.sphinxsidebar ul {
- padding-left: 1.5em;
- margin-top: 7px;
- padding: 0;
- line-height: 130%;
-}
-
-div.sphinxsidebar ul ul {
- margin-left: 20px;
-}
-
-div.footer {
- background-color: #E0E8D4;
- color: #86989B;
- padding: 3px 8px 3px 0;
- clear: both;
- font-size: 0.8em;
- text-align: right;
-}
-
-div.footer a {
- color: #86989B;
- text-decoration: underline;
-}
-
-/* -- body styles ----------------------------------------------------------- */
-
-p {
- margin: 0.8em 0 0.5em 0;
-}
-
-a {
- color: #CA7900;
- text-decoration: none;
-}
-
-a:hover {
- color: #2491CF;
-}
-
-div.body a {
- text-decoration: underline;
-}
-
-h1 {
- padding: 0.2em 0 0.2em 0;
- margin: 0.7em 0 0.3em 0;
- font-size: 1.5em;
- color: #157;
- background-color: #F0EFE4;
-}
-
-h2 {
- padding: 0.2em 0 0.2em 0;
- margin: 1.3em 0 0.2em 0;
- font-size: 1.35em;
- padding: 0;
- background-color: #FAFAF0;
-}
-
-h3 {
- padding: 0.2em 0 0.2em 0;
- margin: 1em 0 -0.3em 0;
- font-size: 1.2em;
- background-color: #FBFBF3;
-}
-
-div.body h1 a, div.body h2 a, div.body h3 a, div.body h4 a, div.body h5 a, div.body h6 a {
- color: black!important;
-}
-
-h1 a.anchor, h2 a.anchor, h3 a.anchor, h4 a.anchor, h5 a.anchor, h6 a.anchor {
- display: none;
- margin: 0 0 0 0.3em;
- padding: 0 0.2em 0 0.2em;
- color: #aaa!important;
-}
-
-h1:hover a.anchor, h2:hover a.anchor, h3:hover a.anchor, h4:hover a.anchor,
-h5:hover a.anchor, h6:hover a.anchor {
- display: inline;
-}
-
-h1 a.anchor:hover, h2 a.anchor:hover, h3 a.anchor:hover, h4 a.anchor:hover,
-h5 a.anchor:hover, h6 a.anchor:hover {
- color: #777;
- background-color: #eee;
-}
-
-a.headerlink {
- color: #c60f0f!important;
- font-size: 1em;
- margin-left: 6px;
- padding: 0 4px 0 4px;
- text-decoration: none!important;
-}
-
-a.headerlink:hover {
- background-color: #ccc;
- color: white!important;
-}
-
-cite, code, tt {
- font-family: 'Consolas', 'Deja Vu Sans Mono',
- 'Bitstream Vera Sans Mono', monospace;
- font-size: 0.95em;
- letter-spacing: 0.01em;
-}
-
-tt {
- background-color: #f2f2f2;
- border-bottom: 1px solid #ddd;
- color: #333;
-}
-
-tt.descname, tt.descclassname, tt.xref {
- border: 0;
-}
-
-hr {
- border: 1px solid #abc;
- margin: 2em;
-}
-
-a tt {
- border: 0;
- color: #CA7900;
-}
-
-a tt:hover {
- color: #2491CF;
-}
-
-pre {
- font-family: 'Consolas', 'Deja Vu Sans Mono',
- 'Bitstream Vera Sans Mono', monospace;
- font-size: 0.95em;
- letter-spacing: 0.015em;
- line-height: 120%;
- padding: 0.5em;
- border: 1px solid #ccc;
- background-color: #f8f8f8;
-}
-
-pre a {
- color: inherit;
- text-decoration: underline;
-}
-
-td.linenos pre {
- padding: 0.5em 0;
-}
-
-div.quotebar {
- background-color: #f8f8f8;
- max-width: 250px;
- float: right;
- padding: 2px 7px;
- border: 1px solid #ccc;
-}
-
-div.topic {
- background-color: #f8f8f8;
-}
-
-table {
- border-collapse: collapse;
- margin: 0 -0.5em 0 -0.5em;
-}
-
-table td, table th {
- padding: 0.2em 0.5em 0.2em 0.5em;
-}
-
-div.admonition, div.warning {
- font-size: 0.9em;
- margin: 1em 0 1em 0;
- border: 1px solid #86989B;
- background-color: #f7f7f7;
- padding: 0;
-}
-
-div.admonition p, div.warning p {
- margin: 0.5em 1em 0.5em 1em;
- padding: 0;
-}
-
-div.admonition pre, div.warning pre {
- margin: 0.4em 1em 0.4em 1em;
-}
-
-div.admonition p.admonition-title,
-div.warning p.admonition-title {
- margin: 0;
- padding: 0.1em 0 0.1em 0.5em;
- color: white;
- border-bottom: 1px solid #86989B;
- font-weight: bold;
- background-color: #AFC1C4;
-}
-
-div.warning {
- border: 1px solid #940000;
-}
-
-div.warning p.admonition-title {
- background-color: #CF0000;
- border-bottom-color: #940000;
-}
-
-div.admonition ul, div.admonition ol,
-div.warning ul, div.warning ol {
- margin: 0.1em 0.5em 0.5em 3em;
- padding: 0;
-}
-
-div.versioninfo {
- margin: 1em 0 0 0;
- border: 1px solid #ccc;
- background-color: #DDEAF0;
- padding: 8px;
- line-height: 1.3em;
- font-size: 0.9em;
-}
-
-.viewcode-back {
- font-family: 'Lucida Grande', 'Lucida Sans Unicode', 'Geneva',
- 'Verdana', sans-serif;
-}
-
-div.viewcode-block:target {
- background-color: #f4debf;
- border-top: 1px solid #ac9;
- border-bottom: 1px solid #ac9;
-}
+/*
+ * lmfitdoc.css_t
+ * minor riff on sphinxdoc.css_t
+ * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ *
+ * Sphinx stylesheet -- sphinxdoc theme. Originally created by
+ * Armin Ronacher for Werkzeug.
+ *
+ * :copyright: Copyright 2007-2014 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+ at import url("basic.css");
+
+/* -- page layout ----------------------------------------------------------- */
+
+body {
+ font-family: 'Lucida Grande', 'Lucida Sans Unicode', 'Geneva', 'Verdana', sans-serif;
+ font-size: 14px;
+ letter-spacing: -0.01em;
+ line-height: 150%;
+ text-align: center;
+ background-color: #D6DAC4;
+ color: black;
+ padding: 0;
+ border: 0px solid #D0D0C0;
+ margin: 15px 15px 15px 15px;
+ min-width: 740px;
+}
+
+div.document {
+ background-color: white;
+ text-align: left;
+ background-image: url(contents.png);
+ background-repeat: repeat-x;
+}
+
+div.bodywrapper {
+ margin: 0 {{ theme_sidebarwidth|toint + 10 }}px 0 0;
+ border-right: 1px solid #ccc;
+}
+
+div.body {
+ margin: 0;
+ padding: 0.5em 20px 20px 20px;
+}
+
+div.related {
+ font-size: 1em;
+ background-color: #0D0;
+}
+
+div.related ul {
+ height: 2em;
+ border-top: 1px solid #ddd;
+ border-bottom: 1px solid #ddd;
+ background-color: #F0EFE4;
+ color: #157;
+}
+
+div.related ul li {
+ margin: 0;
+ padding: 0;
+ height: 2em;
+ float: left;
+ background-color: #D0000;
+}
+
+div.related ul li.right {
+ float: right;
+ margin-right: 5px;
+}
+
+div.related ul li a {
+ margin: 0;
+ padding: 0 5px 0 5px;
+ line-height: 1.75em;
+ color: #EE9816;
+ color: #157;
+}
+
+div.related ul li a:hover {
+ color: #822;
+}
+
+div.sphinxsidebarwrapper {
+ padding: 0;
+}
+
+div.sphinxsidebar {
+ margin: 0;
+ padding: 0.5em 15px 15px 0;
+ width: {{ theme_sidebarwidth|toint - 20 }}px;
+ float: right;
+ font-size: 1em;
+ text-align: left;
+}
+
+div.sphinxsidebar h3, div.sphinxsidebar h4 {
+ margin: 1em 0 0.5em 0;
+ font-size: 1em;
+ padding: 0.1em 0 0.1em 0.5em;
+ color: #157;
+ border: 1px solid #A0A090;
+ background-color: #D0D0C4;
+}
+
+div.sphinxsidebar h3 a {
+ color: #157;
+ background-color: #D0D0C4;
+}
+
+div.sphinxsidebar ul {
+ padding-left: 1.5em;
+ margin-top: 7px;
+ padding: 0;
+ line-height: 130%;
+}
+
+div.sphinxsidebar ul ul {
+ margin-left: 20px;
+}
+
+div.footer {
+ background-color: #E0E8D4;
+ color: #86989B;
+ padding: 3px 8px 3px 0;
+ clear: both;
+ font-size: 0.8em;
+ text-align: right;
+}
+
+div.footer a {
+ color: #86989B;
+ text-decoration: underline;
+}
+
+/* -- body styles ----------------------------------------------------------- */
+
+p {
+ margin: 0.8em 0 0.5em 0;
+}
+
+a {
+ color: #CA7900;
+ text-decoration: none;
+}
+
+a:hover {
+ color: #2491CF;
+}
+
+div.body a {
+ text-decoration: underline;
+}
+
+h1 {
+ padding: 0.2em 0 0.2em 0;
+ margin: 0.7em 0 0.3em 0;
+ font-size: 1.5em;
+ color: #157;
+ background-color: #F0EFE4;
+}
+
+h2 {
+ padding: 0.2em 0 0.2em 0;
+ margin: 1.3em 0 0.2em 0;
+ font-size: 1.35em;
+ padding: 0;
+ background-color: #FAFAF0;
+}
+
+h3 {
+ padding: 0.2em 0 0.2em 0;
+ margin: 1em 0 -0.3em 0;
+ font-size: 1.2em;
+ background-color: #FBFBF3;
+}
+
+div.body h1 a, div.body h2 a, div.body h3 a, div.body h4 a, div.body h5 a, div.body h6 a {
+ color: black!important;
+}
+
+h1 a.anchor, h2 a.anchor, h3 a.anchor, h4 a.anchor, h5 a.anchor, h6 a.anchor {
+ display: none;
+ margin: 0 0 0 0.3em;
+ padding: 0 0.2em 0 0.2em;
+ color: #aaa!important;
+}
+
+h1:hover a.anchor, h2:hover a.anchor, h3:hover a.anchor, h4:hover a.anchor,
+h5:hover a.anchor, h6:hover a.anchor {
+ display: inline;
+}
+
+h1 a.anchor:hover, h2 a.anchor:hover, h3 a.anchor:hover, h4 a.anchor:hover,
+h5 a.anchor:hover, h6 a.anchor:hover {
+ color: #777;
+ background-color: #eee;
+}
+
+a.headerlink {
+ color: #c60f0f!important;
+ font-size: 1em;
+ margin-left: 6px;
+ padding: 0 4px 0 4px;
+ text-decoration: none!important;
+}
+
+a.headerlink:hover {
+ background-color: #ccc;
+ color: white!important;
+}
+
+cite, code, tt {
+ font-family: 'Consolas', 'Deja Vu Sans Mono',
+ 'Bitstream Vera Sans Mono', monospace;
+ font-size: 0.95em;
+ letter-spacing: 0.01em;
+}
+
+tt {
+ background-color: #f2f2f2;
+ border-bottom: 1px solid #ddd;
+ color: #333;
+}
+
+tt.descname, tt.descclassname, tt.xref {
+ border: 0;
+}
+
+hr {
+ border: 1px solid #abc;
+ margin: 2em;
+}
+
+a tt {
+ border: 0;
+ color: #CA7900;
+}
+
+a tt:hover {
+ color: #2491CF;
+}
+
+pre {
+ font-family: 'Consolas', 'Deja Vu Sans Mono',
+ 'Bitstream Vera Sans Mono', monospace;
+ font-size: 0.95em;
+ letter-spacing: 0.015em;
+ line-height: 120%;
+ padding: 0.5em;
+ border: 1px solid #ccc;
+ background-color: #f8f8f8;
+}
+
+pre a {
+ color: inherit;
+ text-decoration: underline;
+}
+
+td.linenos pre {
+ padding: 0.5em 0;
+}
+
+div.quotebar {
+ background-color: #f8f8f8;
+ max-width: 250px;
+ float: right;
+ padding: 2px 7px;
+ border: 1px solid #ccc;
+}
+
+div.topic {
+ background-color: #f8f8f8;
+}
+
+table {
+ border-collapse: collapse;
+ margin: 0 -0.5em 0 -0.5em;
+}
+
+table td, table th {
+ padding: 0.2em 0.5em 0.2em 0.5em;
+}
+
+div.admonition, div.warning {
+ font-size: 0.9em;
+ margin: 1em 0 1em 0;
+ border: 1px solid #86989B;
+ background-color: #f7f7f7;
+ padding: 0;
+}
+
+div.admonition p, div.warning p {
+ margin: 0.5em 1em 0.5em 1em;
+ padding: 0;
+}
+
+div.admonition pre, div.warning pre {
+ margin: 0.4em 1em 0.4em 1em;
+}
+
+div.admonition p.admonition-title,
+div.warning p.admonition-title {
+ margin: 0;
+ padding: 0.1em 0 0.1em 0.5em;
+ color: white;
+ border-bottom: 1px solid #86989B;
+ font-weight: bold;
+ background-color: #AFC1C4;
+}
+
+div.warning {
+ border: 1px solid #940000;
+}
+
+div.warning p.admonition-title {
+ background-color: #CF0000;
+ border-bottom-color: #940000;
+}
+
+div.admonition ul, div.admonition ol,
+div.warning ul, div.warning ol {
+ margin: 0.1em 0.5em 0.5em 3em;
+ padding: 0;
+}
+
+div.versioninfo {
+ margin: 1em 0 0 0;
+ border: 1px solid #ccc;
+ background-color: #DDEAF0;
+ padding: 8px;
+ line-height: 1.3em;
+ font-size: 0.9em;
+}
+
+.viewcode-back {
+ font-family: 'Lucida Grande', 'Lucida Sans Unicode', 'Geneva',
+ 'Verdana', sans-serif;
+}
+
+div.viewcode-block:target {
+ background-color: #f4debf;
+ border-top: 1px solid #ac9;
+ border-bottom: 1px solid #ac9;
+}
diff --git a/doc/sphinx/theme/lmfitdoc/theme.conf b/doc/sphinx/theme/lmfitdoc/theme.conf
index 82db5fb..d3bfaad 100644
--- a/doc/sphinx/theme/lmfitdoc/theme.conf
+++ b/doc/sphinx/theme/lmfitdoc/theme.conf
@@ -1,4 +1,4 @@
-[theme]
-inherit = basic
-stylesheet = lmfitdoc.css
-pygments_style = friendly
+[theme]
+inherit = basic
+stylesheet = lmfitdoc.css
+pygments_style = friendly
diff --git a/doc/support.rst b/doc/support.rst
index 9a08328..4fe2c3e 100644
--- a/doc/support.rst
+++ b/doc/support.rst
@@ -1,30 +1,30 @@
-.. _support_chapter:
-
-===========================
-Getting Help
-===========================
-
-.. _mailing list: https://groups.google.com/group/lmfit-py
-.. _github issues: https://github.com/lmfit/lmfit-py/issues
-
-If you have questions, comments, or suggestions for LMFIT, please use the
-`mailing list`_. This provides an on-line conversation that is and
-archived well and can be searched well with standard web searches. If you
-find a bug with the code or documentation, use the `github issues`_ Issue
-tracker to submit a report. If you have an idea for how to solve the
-problem and are familiar with python and github, submitting a github Pull
-Request would be greatly appreciated.
-
-If you are unsure whether to use the mailing list or the Issue tracker,
-please start a conversation on the `mailing list`_. That is, the problem
-you're having may or may not be due to a bug. If it is due to a bug,
-creating an Issue from the conversation is easy. If it is not a bug, the
-problem will be discussed and then the Issue will be closed. While one
-*can* search through closed Issues on github, these are not so easily
-searched, and the conversation is not easily useful to others later.
-Starting the conversation on the mailing list with "How do I do this?" or
-"Why didn't this work?" instead of "This should work and doesn't" is
-generally preferred, and will better help others with similar questions.
-Of course, there is not always an obvious way to decide if something is a
-Question or an Issue, and we will try our best to engage in all
-discussions.
+.. _support_chapter:
+
+===========================
+Getting Help
+===========================
+
+.. _mailing list: https://groups.google.com/group/lmfit-py
+.. _github issues: https://github.com/lmfit/lmfit-py/issues
+
+If you have questions, comments, or suggestions for LMFIT, please use the
+`mailing list`_. This provides an on-line conversation that is and
+archived well and can be searched well with standard web searches. If you
+find a bug with the code or documentation, use the `github issues`_ Issue
+tracker to submit a report. If you have an idea for how to solve the
+problem and are familiar with python and github, submitting a github Pull
+Request would be greatly appreciated.
+
+If you are unsure whether to use the mailing list or the Issue tracker,
+please start a conversation on the `mailing list`_. That is, the problem
+you're having may or may not be due to a bug. If it is due to a bug,
+creating an Issue from the conversation is easy. If it is not a bug, the
+problem will be discussed and then the Issue will be closed. While one
+*can* search through closed Issues on github, these are not so easily
+searched, and the conversation is not easily useful to others later.
+Starting the conversation on the mailing list with "How do I do this?" or
+"Why didn't this work?" instead of "This should work and doesn't" is
+generally preferred, and will better help others with similar questions.
+Of course, there is not always an obvious way to decide if something is a
+Question or an Issue, and we will try our best to engage in all
+discussions.
diff --git a/doc/whatsnew.rst b/doc/whatsnew.rst
index 2d94a51..125f2c7 100644
--- a/doc/whatsnew.rst
+++ b/doc/whatsnew.rst
@@ -1,97 +1,97 @@
-.. _whatsnew_chapter:
-
-=====================
-Release Notes
-=====================
-
-.. _lmfit github repository: http://github.com/lmfit/lmfit-py
-
-This section discusses changes between versions, especially significant
-changes to the use and behavior of the library. This is not meant to be a
-comprehensive list of changes. For such a complete record, consult the
-`lmfit github repository`_.
-
-.. _whatsnew_090_label:
-
-Version 0.9.0 Release Notes
-==========================================
-
-This upgrade makes an important, non-backward-compatible change to the way
-many fitting scripts and programs will work. Scripts that work with
-version 0.8.3 will not work with version 0.9.0 and vice versa. The change
-was not made lightly or without ample discussion, and is really an
-improvement. Modifying scripts that did work with 0.8.3 to work with 0.9.0
-is easy, but needs to be done.
-
-
-
-Summary
-~~~~~~~~~~~~
-
-The upgrade from 0.8.3 to 0.9.0 introduced the :class:`MinimizerResult`
-class (see :ref:`fit-results-label`) which is now used to hold the return
-value from :func:`minimize` and :meth:`Minimizer.minimize`. This returned
-object contains many goodness of fit statistics, and holds the optimized
-parameters from the fit. Importantly, the parameters passed into
-:func:`minimize` and :meth:`Minimizer.minimize` are no longer modified by
-the fit. Instead, a copy of the passed-in parameters is made which is
-changed and returns as the :attr:`params` attribute of the returned
-:class:`MinimizerResult`.
-
-
-Impact
-~~~~~~~~~~~~~
-
-This upgrade means that a script that does::
-
- my_pars = Parameters()
- my_pars.add('amp', value=300.0, min=0)
- my_pars.add('center', value= 5.0, min=0, max=10)
- my_pars.add('decay', value= 1.0, vary=False)
-
- result = minimize(objfunc, my_pars)
-
-will still work, but that ``my_pars`` will **NOT** be changed by the fit.
-Instead, ``my_pars`` is copied to an internal set of parameters that is
-changed in the fit, and this copy is then put in ``result.params``. To
-look at fit results, use ``result.params``, not ``my_pars``.
-
-This has the effect that ``my_pars`` will still hold the starting parameter
-values, while all of the results from the fit are held in the ``result``
-object returned by :func:`minimize`.
-
-If you want to do an initial fit, then refine that fit to, for example, do
-a pre-fit, then refine that result different fitting method, such as::
-
- result1 = minimize(objfunc, my_pars, method='nelder')
- result1.params['decay'].vary = True
- result2 = minimize(objfunc, result1.params, method='leastsq')
-
-and have access to all of the starting parameters ``my_pars``, the result of the
-first fit ``result1``, and the result of the final fit ``result2``.
-
-
-
-Discussion
-~~~~~~~~~~~~~~
-
-The main goal for making this change were to
-
- 1. give a better return value to :func:`minimize` and
- :meth:`Minimizer.minimize` that can hold all of the information
- about a fit. By having the return value be an instance of the
- :class:`MinimizerResult` class, it can hold an arbitrary amount of
- information that is easily accessed by attribute name, and even
- be given methods. Using objects is good!
-
- 2. To limit or even elimate the amount of "state information" a
- :class:`Minimizer` holds. By state information, we mean how much of
- the previous fit is remembered after a fit is done. Keeping (and
- especially using) such information about a previous fit means that
- a :class:`Minimizer` might give different results even for the same
- problem if run a second time. While it's desirable to be able to
- adjust a set of :class:`Parameters` re-run a fit to get an improved
- result, doing this by changing an *internal attribute
- (:attr:`Minimizer.params`) has the undesirable side-effect of not
- being able to "go back", and makes it somewhat cumbersome to keep
- track of changes made while adjusting parameters and re-running fits.
+.. _whatsnew_chapter:
+
+=====================
+Release Notes
+=====================
+
+.. _lmfit github repository: http://github.com/lmfit/lmfit-py
+
+This section discusses changes between versions, especially significant
+changes to the use and behavior of the library. This is not meant to be a
+comprehensive list of changes. For such a complete record, consult the
+`lmfit github repository`_.
+
+.. _whatsnew_090_label:
+
+Version 0.9.0 Release Notes
+==========================================
+
+This upgrade makes an important, non-backward-compatible change to the way
+many fitting scripts and programs will work. Scripts that work with
+version 0.8.3 will not work with version 0.9.0 and vice versa. The change
+was not made lightly or without ample discussion, and is really an
+improvement. Modifying scripts that did work with 0.8.3 to work with 0.9.0
+is easy, but needs to be done.
+
+
+
+Summary
+~~~~~~~~~~~~
+
+The upgrade from 0.8.3 to 0.9.0 introduced the :class:`MinimizerResult`
+class (see :ref:`fit-results-label`) which is now used to hold the return
+value from :func:`minimize` and :meth:`Minimizer.minimize`. This returned
+object contains many goodness of fit statistics, and holds the optimized
+parameters from the fit. Importantly, the parameters passed into
+:func:`minimize` and :meth:`Minimizer.minimize` are no longer modified by
+the fit. Instead, a copy of the passed-in parameters is made which is
+changed and returns as the :attr:`params` attribute of the returned
+:class:`MinimizerResult`.
+
+
+Impact
+~~~~~~~~~~~~~
+
+This upgrade means that a script that does::
+
+ my_pars = Parameters()
+ my_pars.add('amp', value=300.0, min=0)
+ my_pars.add('center', value= 5.0, min=0, max=10)
+ my_pars.add('decay', value= 1.0, vary=False)
+
+ result = minimize(objfunc, my_pars)
+
+will still work, but that ``my_pars`` will **NOT** be changed by the fit.
+Instead, ``my_pars`` is copied to an internal set of parameters that is
+changed in the fit, and this copy is then put in ``result.params``. To
+look at fit results, use ``result.params``, not ``my_pars``.
+
+This has the effect that ``my_pars`` will still hold the starting parameter
+values, while all of the results from the fit are held in the ``result``
+object returned by :func:`minimize`.
+
+If you want to do an initial fit, then refine that fit to, for example, do
+a pre-fit, then refine that result different fitting method, such as::
+
+ result1 = minimize(objfunc, my_pars, method='nelder')
+ result1.params['decay'].vary = True
+ result2 = minimize(objfunc, result1.params, method='leastsq')
+
+and have access to all of the starting parameters ``my_pars``, the result of the
+first fit ``result1``, and the result of the final fit ``result2``.
+
+
+
+Discussion
+~~~~~~~~~~~~~~
+
+The main goal for making this change were to
+
+1. give a better return value to :func:`minimize` and
+ :meth:`Minimizer.minimize` that can hold all of the information
+ about a fit. By having the return value be an instance of the
+ :class:`MinimizerResult` class, it can hold an arbitrary amount of
+ information that is easily accessed by attribute name, and even
+ be given methods. Using objects is good!
+
+2. To limit or even eliminate the amount of "state information" a
+ :class:`Minimizer` holds. By state information, we mean how much of
+ the previous fit is remembered after a fit is done. Keeping (and
+ especially using) such information about a previous fit means that
+ a :class:`Minimizer` might give different results even for the same
+ problem if run a second time. While it's desirable to be able to
+ adjust a set of :class:`Parameters` re-run a fit to get an improved
+ result, doing this by changing an internal attribute
+ (:attr:`Minimizer.params`) has the undesirable side-effect of not
+ being able to "go back", and makes it somewhat cumbersome to keep
+ track of changes made while adjusting parameters and re-running fits.
diff --git a/lmfit/__init__.py b/lmfit/__init__.py
index df6a441..30d0d6b 100644
--- a/lmfit/__init__.py
+++ b/lmfit/__init__.py
@@ -1,53 +1,53 @@
-"""
-Lmfit provides a high-level interface to non-linear optimization and curve
-fitting problems for Python. Lmfit builds on Levenberg-Marquardt algorithm of
-scipy.optimize.leastsq(), but also supports most of the optimization methods
-from scipy.optimize. It has a number of useful enhancements, including:
-
- * Using Parameter objects instead of plain floats as variables. A Parameter
- has a value that can be varied in the fit, fixed, have upper and/or lower
- bounds. It can even have a value that is constrained by an algebraic
- expression of other Parameter values.
-
- * Ease of changing fitting algorithms. Once a fitting model is set up, one
- can change the fitting algorithm without changing the objective function.
-
- * Improved estimation of confidence intervals. While
- scipy.optimize.leastsq() will automatically calculate uncertainties and
- correlations from the covariance matrix, lmfit also has functions to
- explicitly explore parameter space to determine confidence levels even for
- the most difficult cases.
-
- * Improved curve-fitting with the Model class. This which extends the
- capabilities of scipy.optimize.curve_fit(), allowing you to turn a function
- that models for your data into a python class that helps you parametrize
- and fit data with that model.
-
- * Many pre-built models for common lineshapes are included and ready to use.
-
- version: 0.8.0
- last update: 2014-Sep-21
- License: MIT
- Authors: Matthew Newville, The University of Chicago
- Till Stensitzki, Freie Universitat Berlin
- Daniel B. Allen, Johns Hopkins University
- Antonino Ingargiola, University of California, Los Angeles
-"""
-
-from .minimizer import minimize, Minimizer, MinimizerException
-from .parameter import Parameter, Parameters
-from .confidence import conf_interval, conf_interval2d
-from .printfuncs import (fit_report, ci_report,
- report_fit, report_ci, report_errors)
-
-from .model import Model, CompositeModel
-from . import models
-
-from . import uncertainties
-from .uncertainties import ufloat, correlated_values
-
-
-## versioneer code
-from ._version import get_versions
-__version__ = get_versions()['version']
-del get_versions
+"""
+Lmfit provides a high-level interface to non-linear optimization and curve
+fitting problems for Python. Lmfit builds on Levenberg-Marquardt algorithm of
+scipy.optimize.leastsq(), but also supports most of the optimization methods
+from scipy.optimize. It has a number of useful enhancements, including:
+
+ * Using Parameter objects instead of plain floats as variables. A Parameter
+ has a value that can be varied in the fit, fixed, have upper and/or lower
+ bounds. It can even have a value that is constrained by an algebraic
+ expression of other Parameter values.
+
+ * Ease of changing fitting algorithms. Once a fitting model is set up, one
+ can change the fitting algorithm without changing the objective function.
+
+ * Improved estimation of confidence intervals. While
+ scipy.optimize.leastsq() will automatically calculate uncertainties and
+ correlations from the covariance matrix, lmfit also has functions to
+ explicitly explore parameter space to determine confidence levels even for
+ the most difficult cases.
+
+ * Improved curve-fitting with the Model class. This which extends the
+ capabilities of scipy.optimize.curve_fit(), allowing you to turn a function
+ that models for your data into a python class that helps you parametrize
+ and fit data with that model.
+
+ * Many pre-built models for common lineshapes are included and ready to use.
+
+ version: 0.8.0
+ last update: 2014-Sep-21
+ License: MIT
+ Authors: Matthew Newville, The University of Chicago
+ Till Stensitzki, Freie Universitat Berlin
+ Daniel B. Allen, Johns Hopkins University
+ Antonino Ingargiola, University of California, Los Angeles
+"""
+
+from .minimizer import minimize, Minimizer, MinimizerException
+from .parameter import Parameter, Parameters
+from .confidence import conf_interval, conf_interval2d
+from .printfuncs import (fit_report, ci_report,
+ report_fit, report_ci, report_errors)
+
+from .model import Model, CompositeModel
+from . import models
+
+from . import uncertainties
+from .uncertainties import ufloat, correlated_values
+
+
+## versioneer code
+from ._version import get_versions
+__version__ = get_versions()['version']
+del get_versions
diff --git a/lmfit/_differentialevolution.py b/lmfit/_differentialevolution.py
index 48f6336..1e1fb66 100644
--- a/lmfit/_differentialevolution.py
+++ b/lmfit/_differentialevolution.py
@@ -1,750 +1,750 @@
-"""
-differential_evolution: The differential evolution global optimization algorithm
-Added by Andrew Nelson 2014
-"""
-from __future__ import division, print_function, absolute_import
-import numpy as np
-from scipy.optimize import minimize
-from scipy.optimize.optimize import _status_message
-import numbers
-
-__all__ = ['differential_evolution']
-
-_MACHEPS = np.finfo(np.float64).eps
-
-
-#------------------------------------------------------------------------------
-# scipy.optimize does not contain OptimizeResult until 0.14. Include here as a
-# fix for scipy < 0.14.
-
-class OptimizeResult(dict):
- """ Represents the optimization result.
- Attributes
- ----------
- x : ndarray
- The solution of the optimization.
- success : bool
- Whether or not the optimizer exited successfully.
- status : int
- Termination status of the optimizer. Its value depends on the
- underlying solver. Refer to `message` for details.
- message : str
- Description of the cause of the termination.
- fun, jac, hess, hess_inv : ndarray
- Values of objective function, Jacobian, Hessian or its inverse (if
- available). The Hessians may be approximations, see the documentation
- of the function in question.
- nfev, njev, nhev : int
- Number of evaluations of the objective functions and of its
- Jacobian and Hessian.
- nit : int
- Number of iterations performed by the optimizer.
- maxcv : float
- The maximum constraint violation.
- Notes
- -----
- There may be additional attributes not listed above depending of the
- specific solver. Since this class is essentially a subclass of dict
- with attribute accessors, one can see which attributes are available
- using the `keys()` method.
- """
- def __getattr__(self, name):
- try:
- return self[name]
- except KeyError:
- raise AttributeError(name)
-
- __setattr__ = dict.__setitem__
- __delattr__ = dict.__delitem__
-
- def __repr__(self):
- if self.keys():
- m = max(map(len, list(self.keys()))) + 1
- return '\n'.join([k.rjust(m) + ': ' + repr(v)
- for k, v in self.items()])
- else:
- return self.__class__.__name__ + "()"
-#------------------------------------------------------------------------------
-
-
-def differential_evolution(func, bounds, args=(), strategy='best1bin',
- maxiter=None, popsize=15, tol=0.01,
- mutation=(0.5, 1), recombination=0.7, seed=None,
- callback=None, disp=False, polish=True,
- init='latinhypercube'):
- """Finds the global minimum of a multivariate function.
- Differential Evolution is stochastic in nature (does not use gradient
- methods) to find the minimium, and can search large areas of candidate
- space, but often requires larger numbers of function evaluations than
- conventional gradient based techniques.
-
- The algorithm is due to Storn and Price [1]_.
-
- Parameters
- ----------
- func : callable
- The objective function to be minimized. Must be in the form
- ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array
- and ``args`` is a tuple of any additional fixed parameters needed to
- completely specify the function.
- bounds : sequence
- Bounds for variables. ``(min, max)`` pairs for each element in ``x``,
- defining the lower and upper bounds for the optimizing argument of
- `func`. It is required to have ``len(bounds) == len(x)``.
- ``len(bounds)`` is used to determine the number of parameters in ``x``.
- args : tuple, optional
- Any additional fixed parameters needed to
- completely specify the objective function.
- strategy : str, optional
- The differential evolution strategy to use. Should be one of:
-
- - 'best1bin'
- - 'best1exp'
- - 'rand1exp'
- - 'randtobest1exp'
- - 'best2exp'
- - 'rand2exp'
- - 'randtobest1bin'
- - 'best2bin'
- - 'rand2bin'
- - 'rand1bin'
-
- The default is 'best1bin'.
- maxiter : int, optional
- The maximum number of times the entire population is evolved.
- The maximum number of function evaluations is:
- ``maxiter * popsize * len(x)``
- popsize : int, optional
- A multiplier for setting the total population size. The population has
- ``popsize * len(x)`` individuals.
- tol : float, optional
- When the mean of the population energies, multiplied by tol,
- divided by the standard deviation of the population energies
- is greater than 1 the solving process terminates:
- ``convergence = mean(pop) * tol / stdev(pop) > 1``
- mutation : float or tuple(float, float), optional
- The mutation constant.
- If specified as a float it should be in the range [0, 2].
- If specified as a tuple ``(min, max)`` dithering is employed. Dithering
- randomly changes the mutation constant on a generation by generation
- basis. The mutation constant for that generation is taken from
- ``U[min, max)``. Dithering can help speed convergence significantly.
- Increasing the mutation constant increases the search radius, but will
- slow down convergence.
- recombination : float, optional
- The recombination constant, should be in the range [0, 1]. Increasing
- this value allows a larger number of mutants to progress into the next
- generation, but at the risk of population stability.
- seed : int or `np.random.RandomState`, optional
- If `seed` is not specified the `np.RandomState` singleton is used.
- If `seed` is an int, a new `np.random.RandomState` instance is used,
- seeded with seed.
- If `seed` is already a `np.random.RandomState instance`, then that
- `np.random.RandomState` instance is used.
- Specify `seed` for repeatable minimizations.
- disp : bool, optional
- Display status messages
- callback : callable, `callback(xk, convergence=val)`, optional:
- A function to follow the progress of the minimization. ``xk`` is
- the current value of ``x0``. ``val`` represents the fractional
- value of the population convergence. When ``val`` is greater than one
- the function halts. If callback returns `True`, then the minimization
- is halted (any polishing is still carried out).
- polish : bool, optional
- If True (default), then `scipy.optimize.minimize` with the `L-BFGS-B`
- method is used to polish the best population member at the end, which
- can improve the minimization slightly.
- init : string, optional
- Specify how the population initialization is performed. Should be
- one of:
-
- - 'latinhypercube'
- - 'random'
-
- The default is 'latinhypercube'. Latin Hypercube sampling tries to
- maximize coverage of the available parameter space. 'random' initializes
- the population randomly - this has the drawback that clustering can
- occur, preventing the whole of parameter space being covered.
-
- Returns
- -------
- res : OptimizeResult
- The optimization result represented as a `OptimizeResult` object.
- Important attributes are: ``x`` the solution array, ``success`` a
- Boolean flag indicating if the optimizer exited successfully and
- ``message`` which describes the cause of the termination. See
- `OptimizeResult` for a description of other attributes. If `polish`
- was employed, then OptimizeResult also contains the `jac` attribute.
-
- Notes
- -----
- Differential evolution is a stochastic population based method that is
- useful for global optimization problems. At each pass through the population
- the algorithm mutates each candidate solution by mixing with other candidate
- solutions to create a trial candidate. There are several strategies [2]_ for
- creating trial candidates, which suit some problems more than others. The
- 'best1bin' strategy is a good starting point for many systems. In this
- strategy two members of the population are randomly chosen. Their difference
- is used to mutate the best member (the `best` in `best1bin`), :math:`b_0`,
- so far:
-
- .. math::
-
- b' = b_0 + mutation * (population[rand0] - population[rand1])
-
- A trial vector is then constructed. Starting with a randomly chosen 'i'th
- parameter the trial is sequentially filled (in modulo) with parameters from
- `b'` or the original candidate. The choice of whether to use `b'` or the
- original candidate is made with a binomial distribution (the 'bin' in
- 'best1bin') - a random number in [0, 1) is generated. If this number is
- less than the `recombination` constant then the parameter is loaded from
- `b'`, otherwise it is loaded from the original candidate. The final
- parameter is always loaded from `b'`. Once the trial candidate is built
- its fitness is assessed. If the trial is better than the original candidate
- then it takes its place. If it is also better than the best overall
- candidate it also replaces that.
- To improve your chances of finding a global minimum use higher `popsize`
- values, with higher `mutation` and (dithering), but lower `recombination`
- values. This has the effect of widening the search radius, but slowing
- convergence.
-
- .. versionadded:: 0.15.0
-
- Examples
- --------
- Let us consider the problem of minimizing the Rosenbrock function. This
- function is implemented in `rosen` in `scipy.optimize`.
-
- >>> from scipy.optimize import rosen, differential_evolution
- >>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)]
- >>> result = differential_evolution(rosen, bounds)
- >>> result.x, result.fun
- (array([1., 1., 1., 1., 1.]), 1.9216496320061384e-19)
-
- Next find the minimum of the Ackley function
- (http://en.wikipedia.org/wiki/Test_functions_for_optimization).
-
- >>> from scipy.optimize import differential_evolution
- >>> import numpy as np
- >>> def ackley(x):
- ... arg1 = -0.2 * np.sqrt(0.5 * (x[0] ** 2 + x[1] ** 2))
- ... arg2 = 0.5 * (np.cos(2. * np.pi * x[0]) + np.cos(2. * np.pi * x[1]))
- ... return -20. * np.exp(arg1) - np.exp(arg2) + 20. + np.e
- >>> bounds = [(-5, 5), (-5, 5)]
- >>> result = differential_evolution(ackley, bounds)
- >>> result.x, result.fun
- (array([ 0., 0.]), 4.4408920985006262e-16)
-
- References
- ----------
- .. [1] Storn, R and Price, K, Differential Evolution - a Simple and
- Efficient Heuristic for Global Optimization over Continuous Spaces,
- Journal of Global Optimization, 1997, 11, 341 - 359.
- .. [2] http://www1.icsi.berkeley.edu/~storn/code.html
- .. [3] http://en.wikipedia.org/wiki/Differential_evolution
- """
-
- solver = DifferentialEvolutionSolver(func, bounds, args=args,
- strategy=strategy, maxiter=maxiter,
- popsize=popsize, tol=tol,
- mutation=mutation,
- recombination=recombination,
- seed=seed, polish=polish,
- callback=callback,
- disp=disp,
- init=init)
- return solver.solve()
-
-
-class DifferentialEvolutionSolver(object):
-
- """This class implements the differential evolution solver
-
- Parameters
- ----------
- func : callable
- The objective function to be minimized. Must be in the form
- ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array
- and ``args`` is a tuple of any additional fixed parameters needed to
- completely specify the function.
- bounds : sequence
- Bounds for variables. ``(min, max)`` pairs for each element in ``x``,
- defining the lower and upper bounds for the optimizing argument of
- `func`. It is required to have ``len(bounds) == len(x)``.
- ``len(bounds)`` is used to determine the number of parameters in ``x``.
- args : tuple, optional
- Any additional fixed parameters needed to
- completely specify the objective function.
- strategy : str, optional
- The differential evolution strategy to use. Should be one of:
-
- - 'best1bin'
- - 'best1exp'
- - 'rand1exp'
- - 'randtobest1exp'
- - 'best2exp'
- - 'rand2exp'
- - 'randtobest1bin'
- - 'best2bin'
- - 'rand2bin'
- - 'rand1bin'
-
- The default is 'best1bin'
-
- maxiter : int, optional
- The maximum number of times the entire population is evolved. The
- maximum number of function evaluations is:
- ``maxiter * popsize * len(x)``
- popsize : int, optional
- A multiplier for setting the total population size. The population has
- ``popsize * len(x)`` individuals.
- tol : float, optional
- When the mean of the population energies, multiplied by tol,
- divided by the standard deviation of the population energies
- is greater than 1 the solving process terminates:
- ``convergence = mean(pop) * tol / stdev(pop) > 1``
- mutation : float or tuple(float, float), optional
- The mutation constant.
- If specified as a float it should be in the range [0, 2].
- If specified as a tuple ``(min, max)`` dithering is employed. Dithering
- randomly changes the mutation constant on a generation by generation
- basis. The mutation constant for that generation is taken from
- U[min, max). Dithering can help speed convergence significantly.
- Increasing the mutation constant increases the search radius, but will
- slow down convergence.
- recombination : float, optional
- The recombination constant, should be in the range [0, 1]. Increasing
- this value allows a larger number of mutants to progress into the next
- generation, but at the risk of population stability.
- seed : int or `np.random.RandomState`, optional
- If `seed` is not specified the `np.random.RandomState` singleton is
- used.
- If `seed` is an int, a new `np.random.RandomState` instance is used,
- seeded with `seed`.
- If `seed` is already a `np.random.RandomState` instance, then that
- `np.random.RandomState` instance is used.
- Specify `seed` for repeatable minimizations.
- disp : bool, optional
- Display status messages
- callback : callable, `callback(xk, convergence=val)`, optional
- A function to follow the progress of the minimization. ``xk`` is
- the current value of ``x0``. ``val`` represents the fractional
- value of the population convergence. When ``val`` is greater than one
- the function halts. If callback returns `True`, then the minimization
- is halted (any polishing is still carried out).
- polish : bool, optional
- If True, then `scipy.optimize.minimize` with the `L-BFGS-B` method
- is used to polish the best population member at the end. This requires
- a few more function evaluations.
- maxfun : int, optional
- Set the maximum number of function evaluations. However, it probably
- makes more sense to set `maxiter` instead.
- init : string, optional
- Specify which type of population initialization is performed. Should be
- one of:
-
- - 'latinhypercube'
- - 'random'
- """
-
- # Dispatch of mutation strategy method (binomial or exponential).
- _binomial = {'best1bin': '_best1',
- 'randtobest1bin': '_randtobest1',
- 'best2bin': '_best2',
- 'rand2bin': '_rand2',
- 'rand1bin': '_rand1'}
- _exponential = {'best1exp': '_best1',
- 'rand1exp': '_rand1',
- 'randtobest1exp': '_randtobest1',
- 'best2exp': '_best2',
- 'rand2exp': '_rand2'}
-
- def __init__(self, func, bounds, args=(),
- strategy='best1bin', maxiter=None, popsize=15,
- tol=0.01, mutation=(0.5, 1), recombination=0.7, seed=None,
- maxfun=None, callback=None, disp=False, polish=True,
- init='latinhypercube'):
-
- if strategy in self._binomial:
- self.mutation_func = getattr(self, self._binomial[strategy])
- elif strategy in self._exponential:
- self.mutation_func = getattr(self, self._exponential[strategy])
- else:
- raise ValueError("Please select a valid mutation strategy")
- self.strategy = strategy
-
- self.callback = callback
- self.polish = polish
- self.tol = tol
-
- #Mutation constant should be in [0, 2). If specified as a sequence
- #then dithering is performed.
- self.scale = mutation
- if (not np.all(np.isfinite(mutation)) or
- np.any(np.array(mutation) >= 2) or
- np.any(np.array(mutation) < 0)):
- raise ValueError('The mutation constant must be a float in '
- 'U[0, 2), or specified as a tuple(min, max)'
- ' where min < max and min, max are in U[0, 2).')
-
- self.dither = None
- if hasattr(mutation, '__iter__') and len(mutation) > 1:
- self.dither = [mutation[0], mutation[1]]
- self.dither.sort()
-
- self.cross_over_probability = recombination
-
- self.func = func
- self.args = args
-
- # convert tuple of lower and upper bounds to limits
- # [(low_0, high_0), ..., (low_n, high_n]
- # -> [[low_0, ..., low_n], [high_0, ..., high_n]]
- self.limits = np.array(bounds, dtype='float').T
- if (np.size(self.limits, 0) != 2
- or not np.all(np.isfinite(self.limits))):
- raise ValueError('bounds should be a sequence containing '
- 'real valued (min, max) pairs for each value'
- ' in x')
-
- self.maxiter = maxiter or 1000
- self.maxfun = (maxfun or ((self.maxiter + 1) * popsize *
- np.size(self.limits, 1)))
-
- # population is scaled to between [0, 1].
- # We have to scale between parameter <-> population
- # save these arguments for _scale_parameter and
- # _unscale_parameter. This is an optimization
- self.__scale_arg1 = 0.5 * (self.limits[0] + self.limits[1])
- self.__scale_arg2 = np.fabs(self.limits[0] - self.limits[1])
-
- parameter_count = np.size(self.limits, 1)
- self.random_number_generator = _make_random_gen(seed)
-
- #default initialization is a latin hypercube design, but there
- #are other population initializations possible.
- self.population = np.zeros((popsize * parameter_count,
- parameter_count))
- if init == 'latinhypercube':
- self.init_population_lhs()
- elif init == 'random':
- self.init_population_random()
- else:
- raise ValueError("The population initialization method must be one"
- "of 'latinhypercube' or 'random'")
-
- self.population_energies = np.ones(
- popsize * parameter_count) * np.inf
-
- self.disp = disp
-
- def init_population_lhs(self):
- """
- Initializes the population with Latin Hypercube Sampling
- Latin Hypercube Sampling ensures that the sampling of parameter space
- is maximised.
- """
- samples = np.size(self.population, 0)
- N = np.size(self.population, 1)
- rng = self.random_number_generator
-
- # Generate the intervals
- segsize = 1.0 / samples
-
- # Fill points uniformly in each interval
- rdrange = rng.rand(samples, N) * segsize
- rdrange += np.atleast_2d(np.arange(0., 1., segsize)).T
-
- # Make the random pairings
- self.population = np.zeros_like(rdrange)
-
- for j in range(N):
- order = rng.permutation(range(samples))
- self.population[:, j] = rdrange[order, j]
-
- def init_population_random(self):
- """
- Initialises the population at random. This type of initialization
- can possess clustering, Latin Hypercube sampling is generally better.
- """
- rng = self.random_number_generator
- self.population = rng.random_sample(self.population.shape)
-
- @property
- def x(self):
- """
- The best solution from the solver
-
- Returns
- -------
- x - ndarray
- The best solution from the solver.
- """
- return self._scale_parameters(self.population[0])
-
- def solve(self):
- """
- Runs the DifferentialEvolutionSolver.
-
- Returns
- -------
- res : OptimizeResult
- The optimization result represented as a ``OptimizeResult`` object.
- Important attributes are: ``x`` the solution array, ``success`` a
- Boolean flag indicating if the optimizer exited successfully and
- ``message`` which describes the cause of the termination. See
- `OptimizeResult` for a description of other attributes. If polish
- was employed, then OptimizeResult also contains the ``hess_inv`` and
- ``jac`` attributes.
- """
-
- nfev, nit, warning_flag = 0, 0, False
- status_message = _status_message['success']
-
- # calculate energies to start with
- for index, candidate in enumerate(self.population):
- parameters = self._scale_parameters(candidate)
- self.population_energies[index] = self.func(parameters,
- *self.args)
- nfev += 1
-
- if nfev > self.maxfun:
- warning_flag = True
- status_message = _status_message['maxfev']
- break
-
- minval = np.argmin(self.population_energies)
-
- # put the lowest energy into the best solution position.
- lowest_energy = self.population_energies[minval]
- self.population_energies[minval] = self.population_energies[0]
- self.population_energies[0] = lowest_energy
-
- self.population[[0, minval], :] = self.population[[minval, 0], :]
-
- if warning_flag:
- return OptimizeResult(
- x=self.x,
- fun=self.population_energies[0],
- nfev=nfev,
- nit=nit,
- message=status_message,
- success=(warning_flag != True))
-
- # do the optimisation.
- for nit in range(1, self.maxiter + 1):
- if self.dither is not None:
- self.scale = self.random_number_generator.rand(
- ) * (self.dither[1] - self.dither[0]) + self.dither[0]
- for candidate in range(np.size(self.population, 0)):
- if nfev > self.maxfun:
- warning_flag = True
- status_message = _status_message['maxfev']
- break
-
- trial = self._mutate(candidate)
- self._ensure_constraint(trial)
- parameters = self._scale_parameters(trial)
-
- energy = self.func(parameters, *self.args)
- nfev += 1
-
- if energy < self.population_energies[candidate]:
- self.population[candidate] = trial
- self.population_energies[candidate] = energy
-
- if energy < self.population_energies[0]:
- self.population_energies[0] = energy
- self.population[0] = trial
-
- # stop when the fractional s.d. of the population is less than tol
- # of the mean energy
- convergence = (np.std(self.population_energies) /
- np.abs(np.mean(self.population_energies) +
- _MACHEPS))
-
- if self.disp:
- print("differential_evolution step %d: f(x)= %g"
- % (nit,
- self.population_energies[0]))
-
- if (self.callback and
- self.callback(self._scale_parameters(self.population[0]),
- convergence=self.tol / convergence) is True):
-
- warning_flag = True
- status_message = ('callback function requested stop early '
- 'by returning True')
- break
-
- if convergence < self.tol or warning_flag:
- break
-
- else:
- status_message = _status_message['maxiter']
- warning_flag = True
-
- DE_result = OptimizeResult(
- x=self.x,
- fun=self.population_energies[0],
- nfev=nfev,
- nit=nit,
- message=status_message,
- success=(warning_flag != True))
-
- if self.polish:
- result = minimize(self.func,
- np.copy(DE_result.x),
- method='L-BFGS-B',
- bounds=self.limits.T,
- args=self.args)
-
- nfev += result.nfev
- DE_result.nfev = nfev
-
- if result.fun < DE_result.fun:
- DE_result.fun = result.fun
- DE_result.x = result.x
- DE_result.jac = result.jac
- # to keep internal state consistent
- self.population_energies[0] = result.fun
- self.population[0] = self._unscale_parameters(result.x)
-
- return DE_result
-
- def _scale_parameters(self, trial):
- """
- scale from a number between 0 and 1 to parameters
- """
- return self.__scale_arg1 + (trial - 0.5) * self.__scale_arg2
-
- def _unscale_parameters(self, parameters):
- """
- scale from parameters to a number between 0 and 1.
- """
- return (parameters - self.__scale_arg1) / self.__scale_arg2 + 0.5
-
- def _ensure_constraint(self, trial):
- """
- make sure the parameters lie between the limits
- """
- for index, param in enumerate(trial):
- if param > 1 or param < 0:
- trial[index] = self.random_number_generator.rand()
-
- def _mutate(self, candidate):
- """
- create a trial vector based on a mutation strategy
- """
- trial = np.copy(self.population[candidate])
- parameter_count = np.size(trial, 0)
-
- fill_point = self.random_number_generator.randint(0, parameter_count)
-
- if (self.strategy == 'randtobest1exp'
- or self.strategy == 'randtobest1bin'):
- bprime = self.mutation_func(candidate,
- self._select_samples(candidate, 5))
- else:
- bprime = self.mutation_func(self._select_samples(candidate, 5))
-
- if self.strategy in self._binomial:
- crossovers = self.random_number_generator.rand(parameter_count)
- crossovers = crossovers < self.cross_over_probability
- # the last one is always from the bprime vector for binomial
- # If you fill in modulo with a loop you have to set the last one to
- # true. If you don't use a loop then you can have any random entry
- # be True.
- crossovers[fill_point] = True
- trial = np.where(crossovers, bprime, trial)
- return trial
-
- elif self.strategy in self._exponential:
- i = 0
- while (i < parameter_count and
- self.random_number_generator.rand() <
- self.cross_over_probability):
-
- trial[fill_point] = bprime[fill_point]
- fill_point = (fill_point + 1) % parameter_count
- i += 1
-
- return trial
-
- def _best1(self, samples):
- """
- best1bin, best1exp
- """
- r0, r1 = samples[:2]
- return (self.population[0] + self.scale *
- (self.population[r0] - self.population[r1]))
-
- def _rand1(self, samples):
- """
- rand1bin, rand1exp
- """
- r0, r1, r2 = samples[:3]
- return (self.population[r0] + self.scale *
- (self.population[r1] - self.population[r2]))
-
- def _randtobest1(self, candidate, samples):
- """
- randtobest1bin, randtobest1exp
- """
- r0, r1 = samples[:2]
- bprime = np.copy(self.population[candidate])
- bprime += self.scale * (self.population[0] - bprime)
- bprime += self.scale * (self.population[r0] -
- self.population[r1])
- return bprime
-
- def _best2(self, samples):
- """
- best2bin, best2exp
- """
- r0, r1, r2, r3 = samples[:4]
- bprime = (self.population[0] + self.scale *
- (self.population[r0] + self.population[r1]
- - self.population[r2] - self.population[r3]))
-
- return bprime
-
- def _rand2(self, samples):
- """
- rand2bin, rand2exp
- """
- r0, r1, r2, r3, r4 = samples
- bprime = (self.population[r0] + self.scale *
- (self.population[r1] + self.population[r2] -
- self.population[r3] - self.population[r4]))
-
- return bprime
-
- def _select_samples(self, candidate, number_samples):
- """
- obtain random integers from range(np.size(self.population, 0)),
- without replacement. You can't have the original candidate either.
- """
- idxs = list(range(np.size(self.population, 0)))
- idxs.remove(candidate)
- self.random_number_generator.shuffle(idxs)
- idxs = idxs[:number_samples]
- return idxs
-
-
-def _make_random_gen(seed):
- """Turn seed into a np.random.RandomState instance
-
- If seed is None, return the RandomState singleton used by np.random.
- If seed is an int, return a new RandomState instance seeded with seed.
- If seed is already a RandomState instance, return it.
- Otherwise raise ValueError.
- """
- if seed is None or seed is np.random:
- return np.random.mtrand._rand
- if isinstance(seed, (numbers.Integral, np.integer)):
- return np.random.RandomState(seed)
- if isinstance(seed, np.random.RandomState):
- return seed
- raise ValueError('%r cannot be used to seed a numpy.random.RandomState'
- ' instance' % seed)
+"""
+differential_evolution: The differential evolution global optimization algorithm
+Added by Andrew Nelson 2014
+"""
+from __future__ import division, print_function, absolute_import
+import numpy as np
+from scipy.optimize import minimize
+from scipy.optimize.optimize import _status_message
+import numbers
+
+__all__ = ['differential_evolution']
+
+_MACHEPS = np.finfo(np.float64).eps
+
+
+#------------------------------------------------------------------------------
+# scipy.optimize does not contain OptimizeResult until 0.14. Include here as a
+# fix for scipy < 0.14.
+
+class OptimizeResult(dict):
+ """ Represents the optimization result.
+ Attributes
+ ----------
+ x : ndarray
+ The solution of the optimization.
+ success : bool
+ Whether or not the optimizer exited successfully.
+ status : int
+ Termination status of the optimizer. Its value depends on the
+ underlying solver. Refer to `message` for details.
+ message : str
+ Description of the cause of the termination.
+ fun, jac, hess, hess_inv : ndarray
+ Values of objective function, Jacobian, Hessian or its inverse (if
+ available). The Hessians may be approximations, see the documentation
+ of the function in question.
+ nfev, njev, nhev : int
+ Number of evaluations of the objective functions and of its
+ Jacobian and Hessian.
+ nit : int
+ Number of iterations performed by the optimizer.
+ maxcv : float
+ The maximum constraint violation.
+ Notes
+ -----
+ There may be additional attributes not listed above depending of the
+ specific solver. Since this class is essentially a subclass of dict
+ with attribute accessors, one can see which attributes are available
+ using the `keys()` method.
+ """
+ def __getattr__(self, name):
+ try:
+ return self[name]
+ except KeyError:
+ raise AttributeError(name)
+
+ __setattr__ = dict.__setitem__
+ __delattr__ = dict.__delitem__
+
+ def __repr__(self):
+ if self.keys():
+ m = max(map(len, list(self.keys()))) + 1
+ return '\n'.join([k.rjust(m) + ': ' + repr(v)
+ for k, v in self.items()])
+ else:
+ return self.__class__.__name__ + "()"
+#------------------------------------------------------------------------------
+
+
+def differential_evolution(func, bounds, args=(), strategy='best1bin',
+ maxiter=None, popsize=15, tol=0.01,
+ mutation=(0.5, 1), recombination=0.7, seed=None,
+ callback=None, disp=False, polish=True,
+ init='latinhypercube'):
+ """Finds the global minimum of a multivariate function.
+ Differential Evolution is stochastic in nature (does not use gradient
+ methods) to find the minimium, and can search large areas of candidate
+ space, but often requires larger numbers of function evaluations than
+ conventional gradient based techniques.
+
+ The algorithm is due to Storn and Price [1]_.
+
+ Parameters
+ ----------
+ func : callable
+ The objective function to be minimized. Must be in the form
+ ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array
+ and ``args`` is a tuple of any additional fixed parameters needed to
+ completely specify the function.
+ bounds : sequence
+ Bounds for variables. ``(min, max)`` pairs for each element in ``x``,
+ defining the lower and upper bounds for the optimizing argument of
+ `func`. It is required to have ``len(bounds) == len(x)``.
+ ``len(bounds)`` is used to determine the number of parameters in ``x``.
+ args : tuple, optional
+ Any additional fixed parameters needed to
+ completely specify the objective function.
+ strategy : str, optional
+ The differential evolution strategy to use. Should be one of:
+
+ - 'best1bin'
+ - 'best1exp'
+ - 'rand1exp'
+ - 'randtobest1exp'
+ - 'best2exp'
+ - 'rand2exp'
+ - 'randtobest1bin'
+ - 'best2bin'
+ - 'rand2bin'
+ - 'rand1bin'
+
+ The default is 'best1bin'.
+ maxiter : int, optional
+ The maximum number of times the entire population is evolved.
+ The maximum number of function evaluations is:
+ ``maxiter * popsize * len(x)``
+ popsize : int, optional
+ A multiplier for setting the total population size. The population has
+ ``popsize * len(x)`` individuals.
+ tol : float, optional
+ When the mean of the population energies, multiplied by tol,
+ divided by the standard deviation of the population energies
+ is greater than 1 the solving process terminates:
+ ``convergence = mean(pop) * tol / stdev(pop) > 1``
+ mutation : float or tuple(float, float), optional
+ The mutation constant.
+ If specified as a float it should be in the range [0, 2].
+ If specified as a tuple ``(min, max)`` dithering is employed. Dithering
+ randomly changes the mutation constant on a generation by generation
+ basis. The mutation constant for that generation is taken from
+ ``U[min, max)``. Dithering can help speed convergence significantly.
+ Increasing the mutation constant increases the search radius, but will
+ slow down convergence.
+ recombination : float, optional
+ The recombination constant, should be in the range [0, 1]. Increasing
+ this value allows a larger number of mutants to progress into the next
+ generation, but at the risk of population stability.
+ seed : int or `np.random.RandomState`, optional
+ If `seed` is not specified the `np.RandomState` singleton is used.
+ If `seed` is an int, a new `np.random.RandomState` instance is used,
+ seeded with seed.
+ If `seed` is already a `np.random.RandomState instance`, then that
+ `np.random.RandomState` instance is used.
+ Specify `seed` for repeatable minimizations.
+ disp : bool, optional
+ Display status messages
+ callback : callable, `callback(xk, convergence=val)`, optional:
+ A function to follow the progress of the minimization. ``xk`` is
+ the current value of ``x0``. ``val`` represents the fractional
+ value of the population convergence. When ``val`` is greater than one
+ the function halts. If callback returns `True`, then the minimization
+ is halted (any polishing is still carried out).
+ polish : bool, optional
+ If True (default), then `scipy.optimize.minimize` with the `L-BFGS-B`
+ method is used to polish the best population member at the end, which
+ can improve the minimization slightly.
+ init : string, optional
+ Specify how the population initialization is performed. Should be
+ one of:
+
+ - 'latinhypercube'
+ - 'random'
+
+ The default is 'latinhypercube'. Latin Hypercube sampling tries to
+ maximize coverage of the available parameter space. 'random' initializes
+ the population randomly - this has the drawback that clustering can
+ occur, preventing the whole of parameter space being covered.
+
+ Returns
+ -------
+ res : OptimizeResult
+ The optimization result represented as a `OptimizeResult` object.
+ Important attributes are: ``x`` the solution array, ``success`` a
+ Boolean flag indicating if the optimizer exited successfully and
+ ``message`` which describes the cause of the termination. See
+ `OptimizeResult` for a description of other attributes. If `polish`
+ was employed, then OptimizeResult also contains the `jac` attribute.
+
+ Notes
+ -----
+ Differential evolution is a stochastic population based method that is
+ useful for global optimization problems. At each pass through the population
+ the algorithm mutates each candidate solution by mixing with other candidate
+ solutions to create a trial candidate. There are several strategies [2]_ for
+ creating trial candidates, which suit some problems more than others. The
+ 'best1bin' strategy is a good starting point for many systems. In this
+ strategy two members of the population are randomly chosen. Their difference
+ is used to mutate the best member (the `best` in `best1bin`), :math:`b_0`,
+ so far:
+
+ .. math::
+
+ b' = b_0 + mutation * (population[rand0] - population[rand1])
+
+ A trial vector is then constructed. Starting with a randomly chosen 'i'th
+ parameter the trial is sequentially filled (in modulo) with parameters from
+ `b'` or the original candidate. The choice of whether to use `b'` or the
+ original candidate is made with a binomial distribution (the 'bin' in
+ 'best1bin') - a random number in [0, 1) is generated. If this number is
+ less than the `recombination` constant then the parameter is loaded from
+ `b'`, otherwise it is loaded from the original candidate. The final
+ parameter is always loaded from `b'`. Once the trial candidate is built
+ its fitness is assessed. If the trial is better than the original candidate
+ then it takes its place. If it is also better than the best overall
+ candidate it also replaces that.
+ To improve your chances of finding a global minimum use higher `popsize`
+ values, with higher `mutation` and (dithering), but lower `recombination`
+ values. This has the effect of widening the search radius, but slowing
+ convergence.
+
+ .. versionadded:: 0.15.0
+
+ Examples
+ --------
+ Let us consider the problem of minimizing the Rosenbrock function. This
+ function is implemented in `rosen` in `scipy.optimize`.
+
+ >>> from scipy.optimize import rosen, differential_evolution
+ >>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)]
+ >>> result = differential_evolution(rosen, bounds)
+ >>> result.x, result.fun
+ (array([1., 1., 1., 1., 1.]), 1.9216496320061384e-19)
+
+ Next find the minimum of the Ackley function
+ (http://en.wikipedia.org/wiki/Test_functions_for_optimization).
+
+ >>> from scipy.optimize import differential_evolution
+ >>> import numpy as np
+ >>> def ackley(x):
+ ... arg1 = -0.2 * np.sqrt(0.5 * (x[0] ** 2 + x[1] ** 2))
+ ... arg2 = 0.5 * (np.cos(2. * np.pi * x[0]) + np.cos(2. * np.pi * x[1]))
+ ... return -20. * np.exp(arg1) - np.exp(arg2) + 20. + np.e
+ >>> bounds = [(-5, 5), (-5, 5)]
+ >>> result = differential_evolution(ackley, bounds)
+ >>> result.x, result.fun
+ (array([ 0., 0.]), 4.4408920985006262e-16)
+
+ References
+ ----------
+ .. [1] Storn, R and Price, K, Differential Evolution - a Simple and
+ Efficient Heuristic for Global Optimization over Continuous Spaces,
+ Journal of Global Optimization, 1997, 11, 341 - 359.
+ .. [2] http://www1.icsi.berkeley.edu/~storn/code.html
+ .. [3] http://en.wikipedia.org/wiki/Differential_evolution
+ """
+
+ solver = DifferentialEvolutionSolver(func, bounds, args=args,
+ strategy=strategy, maxiter=maxiter,
+ popsize=popsize, tol=tol,
+ mutation=mutation,
+ recombination=recombination,
+ seed=seed, polish=polish,
+ callback=callback,
+ disp=disp,
+ init=init)
+ return solver.solve()
+
+
+class DifferentialEvolutionSolver(object):
+
+ """This class implements the differential evolution solver
+
+ Parameters
+ ----------
+ func : callable
+ The objective function to be minimized. Must be in the form
+ ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array
+ and ``args`` is a tuple of any additional fixed parameters needed to
+ completely specify the function.
+ bounds : sequence
+ Bounds for variables. ``(min, max)`` pairs for each element in ``x``,
+ defining the lower and upper bounds for the optimizing argument of
+ `func`. It is required to have ``len(bounds) == len(x)``.
+ ``len(bounds)`` is used to determine the number of parameters in ``x``.
+ args : tuple, optional
+ Any additional fixed parameters needed to
+ completely specify the objective function.
+ strategy : str, optional
+ The differential evolution strategy to use. Should be one of:
+
+ - 'best1bin'
+ - 'best1exp'
+ - 'rand1exp'
+ - 'randtobest1exp'
+ - 'best2exp'
+ - 'rand2exp'
+ - 'randtobest1bin'
+ - 'best2bin'
+ - 'rand2bin'
+ - 'rand1bin'
+
+ The default is 'best1bin'
+
+ maxiter : int, optional
+ The maximum number of times the entire population is evolved. The
+ maximum number of function evaluations is:
+ ``maxiter * popsize * len(x)``
+ popsize : int, optional
+ A multiplier for setting the total population size. The population has
+ ``popsize * len(x)`` individuals.
+ tol : float, optional
+ When the mean of the population energies, multiplied by tol,
+ divided by the standard deviation of the population energies
+ is greater than 1 the solving process terminates:
+ ``convergence = mean(pop) * tol / stdev(pop) > 1``
+ mutation : float or tuple(float, float), optional
+ The mutation constant.
+ If specified as a float it should be in the range [0, 2].
+ If specified as a tuple ``(min, max)`` dithering is employed. Dithering
+ randomly changes the mutation constant on a generation by generation
+ basis. The mutation constant for that generation is taken from
+ U[min, max). Dithering can help speed convergence significantly.
+ Increasing the mutation constant increases the search radius, but will
+ slow down convergence.
+ recombination : float, optional
+ The recombination constant, should be in the range [0, 1]. Increasing
+ this value allows a larger number of mutants to progress into the next
+ generation, but at the risk of population stability.
+ seed : int or `np.random.RandomState`, optional
+ If `seed` is not specified the `np.random.RandomState` singleton is
+ used.
+ If `seed` is an int, a new `np.random.RandomState` instance is used,
+ seeded with `seed`.
+ If `seed` is already a `np.random.RandomState` instance, then that
+ `np.random.RandomState` instance is used.
+ Specify `seed` for repeatable minimizations.
+ disp : bool, optional
+ Display status messages
+ callback : callable, `callback(xk, convergence=val)`, optional
+ A function to follow the progress of the minimization. ``xk`` is
+ the current value of ``x0``. ``val`` represents the fractional
+ value of the population convergence. When ``val`` is greater than one
+ the function halts. If callback returns `True`, then the minimization
+ is halted (any polishing is still carried out).
+ polish : bool, optional
+ If True, then `scipy.optimize.minimize` with the `L-BFGS-B` method
+ is used to polish the best population member at the end. This requires
+ a few more function evaluations.
+ maxfun : int, optional
+ Set the maximum number of function evaluations. However, it probably
+ makes more sense to set `maxiter` instead.
+ init : string, optional
+ Specify which type of population initialization is performed. Should be
+ one of:
+
+ - 'latinhypercube'
+ - 'random'
+ """
+
+ # Dispatch of mutation strategy method (binomial or exponential).
+ _binomial = {'best1bin': '_best1',
+ 'randtobest1bin': '_randtobest1',
+ 'best2bin': '_best2',
+ 'rand2bin': '_rand2',
+ 'rand1bin': '_rand1'}
+ _exponential = {'best1exp': '_best1',
+ 'rand1exp': '_rand1',
+ 'randtobest1exp': '_randtobest1',
+ 'best2exp': '_best2',
+ 'rand2exp': '_rand2'}
+
+ def __init__(self, func, bounds, args=(),
+ strategy='best1bin', maxiter=None, popsize=15,
+ tol=0.01, mutation=(0.5, 1), recombination=0.7, seed=None,
+ maxfun=None, callback=None, disp=False, polish=True,
+ init='latinhypercube'):
+
+ if strategy in self._binomial:
+ self.mutation_func = getattr(self, self._binomial[strategy])
+ elif strategy in self._exponential:
+ self.mutation_func = getattr(self, self._exponential[strategy])
+ else:
+ raise ValueError("Please select a valid mutation strategy")
+ self.strategy = strategy
+
+ self.callback = callback
+ self.polish = polish
+ self.tol = tol
+
+ #Mutation constant should be in [0, 2). If specified as a sequence
+ #then dithering is performed.
+ self.scale = mutation
+ if (not np.all(np.isfinite(mutation)) or
+ np.any(np.array(mutation) >= 2) or
+ np.any(np.array(mutation) < 0)):
+ raise ValueError('The mutation constant must be a float in '
+ 'U[0, 2), or specified as a tuple(min, max)'
+ ' where min < max and min, max are in U[0, 2).')
+
+ self.dither = None
+ if hasattr(mutation, '__iter__') and len(mutation) > 1:
+ self.dither = [mutation[0], mutation[1]]
+ self.dither.sort()
+
+ self.cross_over_probability = recombination
+
+ self.func = func
+ self.args = args
+
+ # convert tuple of lower and upper bounds to limits
+ # [(low_0, high_0), ..., (low_n, high_n]
+ # -> [[low_0, ..., low_n], [high_0, ..., high_n]]
+ self.limits = np.array(bounds, dtype='float').T
+ if (np.size(self.limits, 0) != 2
+ or not np.all(np.isfinite(self.limits))):
+ raise ValueError('bounds should be a sequence containing '
+ 'real valued (min, max) pairs for each value'
+ ' in x')
+
+ self.maxiter = maxiter or 1000
+ self.maxfun = (maxfun or ((self.maxiter + 1) * popsize *
+ np.size(self.limits, 1)))
+
+ # population is scaled to between [0, 1].
+ # We have to scale between parameter <-> population
+ # save these arguments for _scale_parameter and
+ # _unscale_parameter. This is an optimization
+ self.__scale_arg1 = 0.5 * (self.limits[0] + self.limits[1])
+ self.__scale_arg2 = np.fabs(self.limits[0] - self.limits[1])
+
+ parameter_count = np.size(self.limits, 1)
+ self.random_number_generator = _make_random_gen(seed)
+
+ #default initialization is a latin hypercube design, but there
+ #are other population initializations possible.
+ self.population = np.zeros((popsize * parameter_count,
+ parameter_count))
+ if init == 'latinhypercube':
+ self.init_population_lhs()
+ elif init == 'random':
+ self.init_population_random()
+ else:
+ raise ValueError("The population initialization method must be one"
+ "of 'latinhypercube' or 'random'")
+
+ self.population_energies = np.ones(
+ popsize * parameter_count) * np.inf
+
+ self.disp = disp
+
+ def init_population_lhs(self):
+ """
+ Initializes the population with Latin Hypercube Sampling
+ Latin Hypercube Sampling ensures that the sampling of parameter space
+ is maximised.
+ """
+ samples = np.size(self.population, 0)
+ N = np.size(self.population, 1)
+ rng = self.random_number_generator
+
+ # Generate the intervals
+ segsize = 1.0 / samples
+
+ # Fill points uniformly in each interval
+ rdrange = rng.rand(samples, N) * segsize
+ rdrange += np.atleast_2d(np.arange(0., 1., segsize)).T
+
+ # Make the random pairings
+ self.population = np.zeros_like(rdrange)
+
+ for j in range(N):
+ order = rng.permutation(range(samples))
+ self.population[:, j] = rdrange[order, j]
+
+ def init_population_random(self):
+ """
+ Initialises the population at random. This type of initialization
+ can possess clustering, Latin Hypercube sampling is generally better.
+ """
+ rng = self.random_number_generator
+ self.population = rng.random_sample(self.population.shape)
+
+ @property
+ def x(self):
+ """
+ The best solution from the solver
+
+ Returns
+ -------
+ x - ndarray
+ The best solution from the solver.
+ """
+ return self._scale_parameters(self.population[0])
+
+ def solve(self):
+ """
+ Runs the DifferentialEvolutionSolver.
+
+ Returns
+ -------
+ res : OptimizeResult
+ The optimization result represented as a ``OptimizeResult`` object.
+ Important attributes are: ``x`` the solution array, ``success`` a
+ Boolean flag indicating if the optimizer exited successfully and
+ ``message`` which describes the cause of the termination. See
+ `OptimizeResult` for a description of other attributes. If polish
+ was employed, then OptimizeResult also contains the ``hess_inv`` and
+ ``jac`` attributes.
+ """
+
+ nfev, nit, warning_flag = 0, 0, False
+ status_message = _status_message['success']
+
+ # calculate energies to start with
+ for index, candidate in enumerate(self.population):
+ parameters = self._scale_parameters(candidate)
+ self.population_energies[index] = self.func(parameters,
+ *self.args)
+ nfev += 1
+
+ if nfev > self.maxfun:
+ warning_flag = True
+ status_message = _status_message['maxfev']
+ break
+
+ minval = np.argmin(self.population_energies)
+
+ # put the lowest energy into the best solution position.
+ lowest_energy = self.population_energies[minval]
+ self.population_energies[minval] = self.population_energies[0]
+ self.population_energies[0] = lowest_energy
+
+ self.population[[0, minval], :] = self.population[[minval, 0], :]
+
+ if warning_flag:
+ return OptimizeResult(
+ x=self.x,
+ fun=self.population_energies[0],
+ nfev=nfev,
+ nit=nit,
+ message=status_message,
+ success=(warning_flag != True))
+
+ # do the optimisation.
+ for nit in range(1, self.maxiter + 1):
+ if self.dither is not None:
+ self.scale = self.random_number_generator.rand(
+ ) * (self.dither[1] - self.dither[0]) + self.dither[0]
+ for candidate in range(np.size(self.population, 0)):
+ if nfev > self.maxfun:
+ warning_flag = True
+ status_message = _status_message['maxfev']
+ break
+
+ trial = self._mutate(candidate)
+ self._ensure_constraint(trial)
+ parameters = self._scale_parameters(trial)
+
+ energy = self.func(parameters, *self.args)
+ nfev += 1
+
+ if energy < self.population_energies[candidate]:
+ self.population[candidate] = trial
+ self.population_energies[candidate] = energy
+
+ if energy < self.population_energies[0]:
+ self.population_energies[0] = energy
+ self.population[0] = trial
+
+ # stop when the fractional s.d. of the population is less than tol
+ # of the mean energy
+ convergence = (np.std(self.population_energies) /
+ np.abs(np.mean(self.population_energies) +
+ _MACHEPS))
+
+ if self.disp:
+ print("differential_evolution step %d: f(x)= %g"
+ % (nit,
+ self.population_energies[0]))
+
+ if (self.callback and
+ self.callback(self._scale_parameters(self.population[0]),
+ convergence=self.tol / convergence) is True):
+
+ warning_flag = True
+ status_message = ('callback function requested stop early '
+ 'by returning True')
+ break
+
+ if convergence < self.tol or warning_flag:
+ break
+
+ else:
+ status_message = _status_message['maxiter']
+ warning_flag = True
+
+ DE_result = OptimizeResult(
+ x=self.x,
+ fun=self.population_energies[0],
+ nfev=nfev,
+ nit=nit,
+ message=status_message,
+ success=(warning_flag != True))
+
+ if self.polish:
+ result = minimize(self.func,
+ np.copy(DE_result.x),
+ method='L-BFGS-B',
+ bounds=self.limits.T,
+ args=self.args)
+
+ nfev += result.nfev
+ DE_result.nfev = nfev
+
+ if result.fun < DE_result.fun:
+ DE_result.fun = result.fun
+ DE_result.x = result.x
+ DE_result.jac = result.jac
+ # to keep internal state consistent
+ self.population_energies[0] = result.fun
+ self.population[0] = self._unscale_parameters(result.x)
+
+ return DE_result
+
+ def _scale_parameters(self, trial):
+ """
+ scale from a number between 0 and 1 to parameters
+ """
+ return self.__scale_arg1 + (trial - 0.5) * self.__scale_arg2
+
+ def _unscale_parameters(self, parameters):
+ """
+ scale from parameters to a number between 0 and 1.
+ """
+ return (parameters - self.__scale_arg1) / self.__scale_arg2 + 0.5
+
+ def _ensure_constraint(self, trial):
+ """
+ make sure the parameters lie between the limits
+ """
+ for index, param in enumerate(trial):
+ if param > 1 or param < 0:
+ trial[index] = self.random_number_generator.rand()
+
+ def _mutate(self, candidate):
+ """
+ create a trial vector based on a mutation strategy
+ """
+ trial = np.copy(self.population[candidate])
+ parameter_count = np.size(trial, 0)
+
+ fill_point = self.random_number_generator.randint(0, parameter_count)
+
+ if (self.strategy == 'randtobest1exp'
+ or self.strategy == 'randtobest1bin'):
+ bprime = self.mutation_func(candidate,
+ self._select_samples(candidate, 5))
+ else:
+ bprime = self.mutation_func(self._select_samples(candidate, 5))
+
+ if self.strategy in self._binomial:
+ crossovers = self.random_number_generator.rand(parameter_count)
+ crossovers = crossovers < self.cross_over_probability
+ # the last one is always from the bprime vector for binomial
+ # If you fill in modulo with a loop you have to set the last one to
+ # true. If you don't use a loop then you can have any random entry
+ # be True.
+ crossovers[fill_point] = True
+ trial = np.where(crossovers, bprime, trial)
+ return trial
+
+ elif self.strategy in self._exponential:
+ i = 0
+ while (i < parameter_count and
+ self.random_number_generator.rand() <
+ self.cross_over_probability):
+
+ trial[fill_point] = bprime[fill_point]
+ fill_point = (fill_point + 1) % parameter_count
+ i += 1
+
+ return trial
+
+ def _best1(self, samples):
+ """
+ best1bin, best1exp
+ """
+ r0, r1 = samples[:2]
+ return (self.population[0] + self.scale *
+ (self.population[r0] - self.population[r1]))
+
+ def _rand1(self, samples):
+ """
+ rand1bin, rand1exp
+ """
+ r0, r1, r2 = samples[:3]
+ return (self.population[r0] + self.scale *
+ (self.population[r1] - self.population[r2]))
+
+ def _randtobest1(self, candidate, samples):
+ """
+ randtobest1bin, randtobest1exp
+ """
+ r0, r1 = samples[:2]
+ bprime = np.copy(self.population[candidate])
+ bprime += self.scale * (self.population[0] - bprime)
+ bprime += self.scale * (self.population[r0] -
+ self.population[r1])
+ return bprime
+
+ def _best2(self, samples):
+ """
+ best2bin, best2exp
+ """
+ r0, r1, r2, r3 = samples[:4]
+ bprime = (self.population[0] + self.scale *
+ (self.population[r0] + self.population[r1]
+ - self.population[r2] - self.population[r3]))
+
+ return bprime
+
+ def _rand2(self, samples):
+ """
+ rand2bin, rand2exp
+ """
+ r0, r1, r2, r3, r4 = samples
+ bprime = (self.population[r0] + self.scale *
+ (self.population[r1] + self.population[r2] -
+ self.population[r3] - self.population[r4]))
+
+ return bprime
+
+ def _select_samples(self, candidate, number_samples):
+ """
+ obtain random integers from range(np.size(self.population, 0)),
+ without replacement. You can't have the original candidate either.
+ """
+ idxs = list(range(np.size(self.population, 0)))
+ idxs.remove(candidate)
+ self.random_number_generator.shuffle(idxs)
+ idxs = idxs[:number_samples]
+ return idxs
+
+
+def _make_random_gen(seed):
+ """Turn seed into a np.random.RandomState instance
+
+ If seed is None, return the RandomState singleton used by np.random.
+ If seed is an int, return a new RandomState instance seeded with seed.
+ If seed is already a RandomState instance, return it.
+ Otherwise raise ValueError.
+ """
+ if seed is None or seed is np.random:
+ return np.random.mtrand._rand
+ if isinstance(seed, (numbers.Integral, np.integer)):
+ return np.random.RandomState(seed)
+ if isinstance(seed, np.random.RandomState):
+ return seed
+ raise ValueError('%r cannot be used to seed a numpy.random.RandomState'
+ ' instance' % seed)
diff --git a/lmfit/_version.py b/lmfit/_version.py
index b0cc39e..fa233a4 100644
--- a/lmfit/_version.py
+++ b/lmfit/_version.py
@@ -4,8 +4,8 @@
# unpacked source archive. Distribution tarballs contain a pre-generated copy
# of this file.
-version_version = '0.9.2'
-version_full = '208871db96689c911e00b9d59dace2de68df3220'
+version_version = '0.9.3'
+version_full = '8a4eb4f5675628bc8ee2d0da70b9e9397f80c280'
def get_versions(default={}, verbose=False):
return {'version': version_version, 'full': version_full}
diff --git a/lmfit/asteval.py b/lmfit/asteval.py
index 87daadc..e8409aa 100644
--- a/lmfit/asteval.py
+++ b/lmfit/asteval.py
@@ -1,802 +1,804 @@
-"""
-Safe(ish) evaluator of python expressions, using ast module.
-The emphasis here is on mathematical expressions, and so
-numpy functions are imported if available and used.
-
-Symbols are held in the Interpreter symtable -- a simple
-dictionary supporting a simple, flat namespace.
-
-Expressions can be compiled into ast node and then evaluated
-later, using the current values in the
-"""
-
-from __future__ import division, print_function
-from sys import exc_info, stdout, version_info
-import ast
-import math
-
-from .astutils import (FROM_PY, FROM_MATH, FROM_NUMPY, UNSAFE_ATTRS,
- LOCALFUNCS, NUMPY_RENAMES, op2func,
- ExceptionHolder, ReturnedNone, valid_symbol_name)
-
-HAS_NUMPY = False
-try:
- import numpy
- HAS_NUMPY = True
-except ImportError:
- print("Warning: numpy not available... functionality will be limited.")
-
-
-class Interpreter:
- """mathematical expression compiler and interpreter.
-
- This module compiles expressions and statements to AST representation,
- using python's ast module, and then executes the AST representation
- using a dictionary of named object (variable, functions).
-
- The result is a restricted, simplified version of Python meant for
- numerical caclulations that is somewhat safer than 'eval' because some
- operations (such as 'import' and 'eval') are simply not allowed. The
- resulting language uses a flat namespace that works on Python objects,
- but does not allow new classes to be defined.
-
- Many parts of Python syntax are supported, including:
- for loops, while loops, if-then-elif-else conditionals
- try-except (including 'finally')
- function definitions with def
- advanced slicing: a[::-1], array[-3:, :, ::2]
- if-expressions: out = one_thing if TEST else other
- list comprehension out = [sqrt(i) for i in values]
-
- The following Python syntax elements are not supported:
- Import, Exec, Lambda, Class, Global, Generators,
- Yield, Decorators
-
- In addition, while many builtin functions are supported, several
- builtin functions are missing ('eval', 'exec', and 'getattr' for
- example) that can be considered unsafe.
-
- If numpy is installed, many numpy functions are also imported.
-
- """
-
- supported_nodes = ('arg', 'assert', 'assign', 'attribute', 'augassign',
- 'binop', 'boolop', 'break', 'call', 'compare',
- 'continue', 'delete', 'dict', 'ellipsis',
- 'excepthandler', 'expr', 'extslice', 'for',
- 'functiondef', 'if', 'ifexp', 'index', 'interrupt',
- 'list', 'listcomp', 'module', 'name', 'num', 'pass',
- 'print', 'raise', 'repr', 'return', 'slice', 'str',
- 'subscript', 'try', 'tuple', 'unaryop', 'while')
-
- def __init__(self, symtable=None, writer=None, use_numpy=True):
- self.writer = writer or stdout
-
- if symtable is None:
- symtable = {}
- self.symtable = symtable
- self._interrupt = None
- self.error = []
- self.error_msg = None
- self.expr = None
- self.retval = None
- self.lineno = 0
- self.use_numpy = HAS_NUMPY and use_numpy
-
- symtable['print'] = self._printer
-
- # add python symbols
- py_symtable = {sym: __builtins__[sym] for sym in FROM_PY
- if sym in __builtins__}
- symtable.update(py_symtable)
-
- # add local symbols
- local_symtable = {sym: obj for (sym, obj) in LOCALFUNCS.items()}
- symtable.update(local_symtable)
-
- # add math symbols
- math_symtable = {sym: getattr(math, sym) for sym in FROM_MATH
- if hasattr(math, sym)}
- symtable.update(math_symtable)
-
- # add numpy symbols
- if self.use_numpy:
- numpy_symtable = {sym: getattr(numpy, sym) for sym in FROM_NUMPY
- if hasattr(numpy, sym)}
- symtable.update(numpy_symtable)
-
- npy_rename_symtable = {name: getattr(numpy, sym) for name, sym
- in NUMPY_RENAMES.items()
- if hasattr(numpy, sym)}
- symtable.update(npy_rename_symtable)
-
- self.node_handlers = dict(((node, getattr(self, "on_%s" % node))
- for node in self.supported_nodes))
-
- # to rationalize try/except try/finally for Python2.6 through Python3.3
- self.node_handlers['tryexcept'] = self.node_handlers['try']
- self.node_handlers['tryfinally'] = self.node_handlers['try']
-
- self.no_deepcopy = [key for key, val in symtable.items()
- if (callable(val)
- or 'numpy.lib.index_tricks' in repr(val))]
-
- def user_defined_symbols(self):
- """
- Return a set of symbols that have been added to symtable after
- construction. I.e. the symbols from self.symtable that are not in
- self.no_deepcopy.
-
- Returns
- -------
- unique_symbols : set
- symbols in symtable that are not in self.no_deepcopy
- """
- sym_in_current = set(self.symtable.keys())
- sym_from_construction = set(self.no_deepcopy)
- unique_symbols = sym_in_current.difference(sym_from_construction)
- return unique_symbols
-
- def unimplemented(self, node):
- "unimplemented nodes"
- self.raise_exception(node, exc=NotImplementedError,
- msg="'%s' not supported" %
- (node.__class__.__name__))
-
- def raise_exception(self, node, exc=None, msg='', expr=None,
- lineno=None):
- "add an exception"
- if self.error is None:
- self.error = []
- if expr is None:
- expr = self.expr
- if len(self.error) > 0 and not isinstance(node, ast.Module):
- msg = '%s' % msg
- err = ExceptionHolder(node, exc=exc, msg=msg, expr=expr, lineno=lineno)
- self._interrupt = ast.Break()
- self.error.append(err)
- if self.error_msg is None:
- self.error_msg = "%s in expr='%s'" % (msg, self.expr)
- elif len(msg) > 0:
- self.error_msg = "%s\n %s" % (self.error_msg, msg)
- if exc is None:
- try:
- exc = self.error[0].exc
- except:
- exc = RuntimeError
- raise exc(self.error_msg)
-
-
- # main entry point for Ast node evaluation
- # parse: text of statements -> ast
- # run: ast -> result
- # eval: string statement -> result = run(parse(statement))
- def parse(self, text):
- """parse statement/expression to Ast representation"""
- self.expr = text
- try:
- return ast.parse(text)
- except SyntaxError:
- self.raise_exception(None, msg='Syntax Error', expr=text)
- except:
- self.raise_exception(None, msg='Runtime Error', expr=text)
-
- def run(self, node, expr=None, lineno=None, with_raise=True):
- """executes parsed Ast representation for an expression"""
- # Note: keep the 'node is None' test: internal code here may run
- # run(None) and expect a None in return.
- if len(self.error) > 0:
- return
- if node is None:
- return None
- if isinstance(node, str):
- node = self.parse(node)
- if lineno is not None:
- self.lineno = lineno
- if expr is not None:
- self.expr = expr
-
- # get handler for this node:
- # on_xxx with handle nodes of type 'xxx', etc
- try:
- handler = self.node_handlers[node.__class__.__name__.lower()]
- except KeyError:
- return self.unimplemented(node)
-
- # run the handler: this will likely generate
- # recursive calls into this run method.
- try:
- ret = handler(node)
- if isinstance(ret, enumerate):
- ret = list(ret)
- return ret
- except:
- if with_raise:
- self.raise_exception(node, expr=expr)
-
- def __call__(self, expr, **kw):
- return self.eval(expr, **kw)
-
- def eval(self, expr, lineno=0, show_errors=True):
- """evaluates a single statement"""
- self.lineno = lineno
- self.error = []
- try:
- node = self.parse(expr)
- except:
- errmsg = exc_info()[1]
- if len(self.error) > 0:
- errmsg = "\n".join(self.error[0].get_error())
- if not show_errors:
- try:
- exc = self.error[0].exc
- except:
- exc = RuntimeError
- raise exc(errmsg)
- print(errmsg, file=self.writer)
- return
- try:
- return self.run(node, expr=expr, lineno=lineno)
- except:
- errmsg = exc_info()[1]
- if len(self.error) > 0:
- errmsg = "\n".join(self.error[0].get_error())
- if not show_errors:
- try:
- exc = self.error[0].exc
- except:
- exc = RuntimeError
- raise exc(errmsg)
- print(errmsg, file=self.writer)
- return
-
- def dump(self, node, **kw):
- "simple ast dumper"
- return ast.dump(node, **kw)
-
- # handlers for ast components
- def on_expr(self, node):
- "expression"
- return self.run(node.value) # ('value',)
-
- def on_index(self, node):
- "index"
- return self.run(node.value) # ('value',)
-
- def on_return(self, node): # ('value',)
- "return statement: look for None, return special sentinal"
- self.retval = self.run(node.value)
- if self.retval is None:
- self.retval = ReturnedNone
- return
-
- def on_repr(self, node):
- "repr "
- return repr(self.run(node.value)) # ('value',)
-
- def on_module(self, node): # ():('body',)
- "module def"
- out = None
- for tnode in node.body:
- out = self.run(tnode)
- return out
-
- def on_pass(self, node):
- "pass statement"
- return None # ()
-
- def on_ellipsis(self, node):
- "ellipses"
- return Ellipsis
-
- # for break and continue: set the instance variable _interrupt
- def on_interrupt(self, node): # ()
- "interrupt handler"
- self._interrupt = node
- return node
-
- def on_break(self, node):
- "break"
- return self.on_interrupt(node)
-
- def on_continue(self, node):
- "continue"
- return self.on_interrupt(node)
-
- def on_assert(self, node): # ('test', 'msg')
- "assert statement"
- if not self.run(node.test):
- self.raise_exception(node, exc=AssertionError, msg=node.msg)
- return True
-
- def on_list(self, node): # ('elt', 'ctx')
- "list"
- return [self.run(e) for e in node.elts]
-
- def on_tuple(self, node): # ('elts', 'ctx')
- "tuple"
- return tuple(self.on_list(node))
-
- def on_dict(self, node): # ('keys', 'values')
- "dictionary"
- return dict([(self.run(k), self.run(v)) for k, v in
- zip(node.keys, node.values)])
-
- def on_num(self, node): # ('n',)
- 'return number'
- return node.n
-
- def on_str(self, node): # ('s',)
- 'return string'
- return node.s
-
- def on_name(self, node): # ('id', 'ctx')
- """ Name node """
- ctx = node.ctx.__class__
- if ctx in (ast.Param, ast.Del):
- return str(node.id)
- else:
- if node.id in self.symtable:
- return self.symtable[node.id]
- else:
- msg = "name '%s' is not defined" % node.id
- self.raise_exception(node, exc=NameError, msg=msg)
-
- def node_assign(self, node, val):
- """here we assign a value (not the node.value object) to a node
- this is used by on_assign, but also by for, list comprehension, etc.
- """
- if node.__class__ == ast.Name:
- if not valid_symbol_name(node.id):
- errmsg = "invalid symbol name (reserved word?) %s" % node.id
- self.raise_exception(node, exc=NameError, msg=errmsg)
- sym = self.symtable[node.id] = val
- if node.id in self.no_deepcopy:
- self.no_deepcopy.pop(node.id)
-
- elif node.__class__ == ast.Attribute:
- if node.ctx.__class__ == ast.Load:
- msg = "cannot assign to attribute %s" % node.attr
- self.raise_exception(node, exc=AttributeError, msg=msg)
-
- setattr(self.run(node.value), node.attr, val)
-
- elif node.__class__ == ast.Subscript:
- sym = self.run(node.value)
- xslice = self.run(node.slice)
- if isinstance(node.slice, ast.Index):
- sym[xslice] = val
- elif isinstance(node.slice, ast.Slice):
- sym[slice(xslice.start, xslice.stop)] = val
- elif isinstance(node.slice, ast.ExtSlice):
- sym[(xslice)] = val
- elif node.__class__ in (ast.Tuple, ast.List):
- if len(val) == len(node.elts):
- for telem, tval in zip(node.elts, val):
- self.node_assign(telem, tval)
- else:
- raise ValueError('too many values to unpack')
-
- def on_attribute(self, node): # ('value', 'attr', 'ctx')
- "extract attribute"
- ctx = node.ctx.__class__
- if ctx == ast.Store:
- msg = "attribute for storage: shouldn't be here!"
- self.raise_exception(node, exc=RuntimeError, msg=msg)
-
- sym = self.run(node.value)
- if ctx == ast.Del:
- return delattr(sym, node.attr)
-
- # ctx is ast.Load
- fmt = "cannnot access attribute '%s' for %s"
- if node.attr not in UNSAFE_ATTRS:
- fmt = "no attribute '%s' for %s"
- try:
- return getattr(sym, node.attr)
- except AttributeError:
- pass
-
- # AttributeError or accessed unsafe attribute
- obj = self.run(node.value)
- msg = fmt % (node.attr, obj)
- self.raise_exception(node, exc=AttributeError, msg=msg)
-
- def on_assign(self, node): # ('targets', 'value')
- "simple assignment"
- val = self.run(node.value)
- for tnode in node.targets:
- self.node_assign(tnode, val)
- return
-
- def on_augassign(self, node): # ('target', 'op', 'value')
- "augmented assign"
- return self.on_assign(ast.Assign(targets=[node.target],
- value=ast.BinOp(left=node.target,
- op=node.op,
- right=node.value)))
-
- def on_slice(self, node): # ():('lower', 'upper', 'step')
- "simple slice"
- return slice(self.run(node.lower),
- self.run(node.upper),
- self.run(node.step))
-
- def on_extslice(self, node): # ():('dims',)
- "extended slice"
- return tuple([self.run(tnode) for tnode in node.dims])
-
- def on_subscript(self, node): # ('value', 'slice', 'ctx')
- "subscript handling -- one of the tricky parts"
- val = self.run(node.value)
- nslice = self.run(node.slice)
- ctx = node.ctx.__class__
- if ctx in (ast.Load, ast.Store):
- if isinstance(node.slice, (ast.Index, ast.Slice, ast.Ellipsis)):
- return val.__getitem__(nslice)
- elif isinstance(node.slice, ast.ExtSlice):
- return val[(nslice)]
- else:
- msg = "subscript with unknown context"
- self.raise_exception(node, msg=msg)
-
- def on_delete(self, node): # ('targets',)
- "delete statement"
- for tnode in node.targets:
- if tnode.ctx.__class__ != ast.Del:
- break
- children = []
- while tnode.__class__ == ast.Attribute:
- children.append(tnode.attr)
- tnode = tnode.value
-
- if tnode.__class__ == ast.Name:
- children.append(tnode.id)
- children.reverse()
- self.symtable.pop('.'.join(children))
- else:
- msg = "could not delete symbol"
- self.raise_exception(node, msg=msg)
-
- def on_unaryop(self, node): # ('op', 'operand')
- "unary operator"
- return op2func(node.op)(self.run(node.operand))
-
- def on_binop(self, node): # ('left', 'op', 'right')
- "binary operator"
- return op2func(node.op)(self.run(node.left),
- self.run(node.right))
-
- def on_boolop(self, node): # ('op', 'values')
- "boolean operator"
- val = self.run(node.values[0])
- is_and = ast.And == node.op.__class__
- if (is_and and val) or (not is_and and not val):
- for n in node.values:
- val = op2func(node.op)(val, self.run(n))
- if (is_and and not val) or (not is_and and val):
- break
- return val
-
- def on_compare(self, node): # ('left', 'ops', 'comparators')
- "comparison operators"
- lval = self.run(node.left)
- out = True
- for op, rnode in zip(node.ops, node.comparators):
- rval = self.run(rnode)
- out = op2func(op)(lval, rval)
- lval = rval
- if self.use_numpy and isinstance(out, numpy.ndarray) and out.any():
- break
- elif not out:
- break
- return out
-
- def on_print(self, node): # ('dest', 'values', 'nl')
- """ note: implements Python2 style print statement, not
- print() function. May need improvement...."""
- dest = self.run(node.dest) or self.writer
- end = ''
- if node.nl:
- end = '\n'
- out = [self.run(tnode) for tnode in node.values]
- if out and len(self.error) == 0:
- self._printer(*out, file=dest, end=end)
-
- def _printer(self, *out, **kws):
- "generic print function"
- flush = kws.pop('flush', True)
- fileh = kws.pop('file', self.writer)
- sep = kws.pop('sep', ' ')
- end = kws.pop('sep', '\n')
-
- print(*out, file=fileh, sep=sep, end=end)
- if flush:
- fileh.flush()
-
- def on_if(self, node): # ('test', 'body', 'orelse')
- "regular if-then-else statement"
- block = node.body
- if not self.run(node.test):
- block = node.orelse
- for tnode in block:
- self.run(tnode)
-
- def on_ifexp(self, node): # ('test', 'body', 'orelse')
- "if expressions"
- expr = node.orelse
- if self.run(node.test):
- expr = node.body
- return self.run(expr)
-
- def on_while(self, node): # ('test', 'body', 'orelse')
- "while blocks"
- while self.run(node.test):
- self._interrupt = None
- for tnode in node.body:
- self.run(tnode)
- if self._interrupt is not None:
- break
- if isinstance(self._interrupt, ast.Break):
- break
- else:
- for tnode in node.orelse:
- self.run(tnode)
- self._interrupt = None
-
- def on_for(self, node): # ('target', 'iter', 'body', 'orelse')
- "for blocks"
- for val in self.run(node.iter):
- self.node_assign(node.target, val)
- self._interrupt = None
- for tnode in node.body:
- self.run(tnode)
- if self._interrupt is not None:
- break
- if isinstance(self._interrupt, ast.Break):
- break
- else:
- for tnode in node.orelse:
- self.run(tnode)
- self._interrupt = None
-
- def on_listcomp(self, node): # ('elt', 'generators')
- "list comprehension"
- out = []
- for tnode in node.generators:
- if tnode.__class__ == ast.comprehension:
- for val in self.run(tnode.iter):
- self.node_assign(tnode.target, val)
- add = True
- for cond in tnode.ifs:
- add = add and self.run(cond)
- if add:
- out.append(self.run(node.elt))
- return out
-
- def on_excepthandler(self, node): # ('type', 'name', 'body')
- "exception handler..."
- return (self.run(node.type), node.name, node.body)
-
- def on_try(self, node): # ('body', 'handlers', 'orelse', 'finalbody')
- "try/except/else/finally blocks"
- no_errors = True
- for tnode in node.body:
- self.run(tnode, with_raise=False)
- no_errors = no_errors and len(self.error) == 0
- if len(self.error) > 0:
- e_type, e_value, e_tback = self.error[-1].exc_info
- for hnd in node.handlers:
- htype = None
- if hnd.type is not None:
- htype = __builtins__.get(hnd.type.id, None)
- if htype is None or isinstance(e_type(), htype):
- self.error = []
- if hnd.name is not None:
- self.node_assign(hnd.name, e_value)
- for tline in hnd.body:
- self.run(tline)
- break
- if no_errors and hasattr(node, 'orelse'):
- for tnode in node.orelse:
- self.run(tnode)
-
- if hasattr(node, 'finalbody'):
- for tnode in node.finalbody:
- self.run(tnode)
-
- def on_raise(self, node): # ('type', 'inst', 'tback')
- "raise statement: note difference for python 2 and 3"
- if version_info[0] == 3:
- excnode = node.exc
- msgnode = node.cause
- else:
- excnode = node.type
- msgnode = node.inst
- out = self.run(excnode)
- msg = ' '.join(out.args)
- msg2 = self.run(msgnode)
- if msg2 not in (None, 'None'):
- msg = "%s: %s" % (msg, msg2)
- self.raise_exception(None, exc=out.__class__, msg=msg, expr='')
-
- def on_call(self, node):
- "function execution"
- # ('func', 'args', 'keywords', 'starargs', 'kwargs')
- func = self.run(node.func)
- if not hasattr(func, '__call__') and not isinstance(func, type):
- msg = "'%s' is not callable!!" % (func)
- self.raise_exception(node, exc=TypeError, msg=msg)
-
- args = [self.run(targ) for targ in node.args]
- if node.starargs is not None:
- args = args + self.run(node.starargs)
-
- keywords = {}
- for key in node.keywords:
- if not isinstance(key, ast.keyword):
- msg = "keyword error in function call '%s'" % (func)
- self.raise_exception(node, msg=msg)
-
- keywords[key.arg] = self.run(key.value)
- if node.kwargs is not None:
- keywords.update(self.run(node.kwargs))
-
- try:
- return func(*args, **keywords)
- except:
- self.raise_exception(node, msg="Error running %s" % (func))
-
- def on_arg(self, node): # ('test', 'msg')
- "arg for function definitions"
- # print(" ON ARG ! ", node, node.arg)
- return node.arg
-
- def on_functiondef(self, node):
- "define procedures"
- # ('name', 'args', 'body', 'decorator_list')
- if node.decorator_list != []:
- raise Warning("decorated procedures not supported!")
- kwargs = []
-
- offset = len(node.args.args) - len(node.args.defaults)
- for idef, defnode in enumerate(node.args.defaults):
- defval = self.run(defnode)
- keyval = self.run(node.args.args[idef+offset])
- kwargs.append((keyval, defval))
-
- if version_info[0] == 3:
- args = [tnode.arg for tnode in node.args.args[:offset]]
- else:
- args = [tnode.id for tnode in node.args.args[:offset]]
-
- doc = None
- nb0 = node.body[0]
- if isinstance(nb0, ast.Expr) and isinstance(nb0.value, ast.Str):
- doc = nb0.value.s
-
- self.symtable[node.name] = Procedure(node.name, self, doc=doc,
- lineno=self.lineno,
- body=node.body,
- args=args, kwargs=kwargs,
- vararg=node.args.vararg,
- varkws=node.args.kwarg)
- if node.name in self.no_deepcopy:
- self.no_deepcopy.pop(node.name)
-
-
-class Procedure(object):
- """Procedure: user-defined function for asteval
-
- This stores the parsed ast nodes as from the
- 'functiondef' ast node for later evaluation.
- """
- def __init__(self, name, interp, doc=None, lineno=0,
- body=None, args=None, kwargs=None,
- vararg=None, varkws=None):
- self.name = name
- self.__asteval__ = interp
- self.raise_exc = self.__asteval__.raise_exception
- self.__doc__ = doc
- self.body = body
- self.argnames = args
- self.kwargs = kwargs
- self.vararg = vararg
- self.varkws = varkws
- self.lineno = lineno
-
- def __repr__(self):
- sig = ""
- if len(self.argnames) > 0:
- sig = "%s%s" % (sig, ', '.join(self.argnames))
- if self.vararg is not None:
- sig = "%s, *%s" % (sig, self.vararg)
- if len(self.kwargs) > 0:
- if len(sig) > 0:
- sig = "%s, " % sig
- _kw = ["%s=%s" % (k, v) for k, v in self.kwargs]
- sig = "%s%s" % (sig, ', '.join(_kw))
-
- if self.varkws is not None:
- sig = "%s, **%s" % (sig, self.varkws)
- sig = "<Procedure %s(%s)>" % (self.name, sig)
- if self.__doc__ is not None:
- sig = "%s\n %s" % (sig, self.__doc__)
- return sig
-
- def __call__(self, *args, **kwargs):
- symlocals = {}
- args = list(args)
- n_args = len(args)
- n_names = len(self.argnames)
- n_kws = len(kwargs)
-
- # may need to move kwargs to args if names align!
- if (n_args < n_names) and n_kws > 0:
- for name in self.argnames[n_args:]:
- if name in kwargs:
- args.append(kwargs.pop(name))
- n_args = len(args)
- n_names = len(self.argnames)
- n_kws = len(kwargs)
-
- if len(self.argnames) > 0 and kwargs is not None:
- msg = "multiple values for keyword argument '%s' in Procedure %s"
- for targ in self.argnames:
- if targ in kwargs:
- self.raise_exc(None, exc=TypeError,
- msg=msg % (targ, self.name),
- lineno=self.lineno)
-
- if n_args != n_names:
- msg = None
- if n_args < n_names:
- msg = 'not enough arguments for Procedure %s()' % self.name
- msg = '%s (expected %i, got %i)' % (msg, n_names, n_args)
- self.raise_exc(None, exc=TypeError, msg=msg)
-
- for argname in self.argnames:
- symlocals[argname] = args.pop(0)
-
- try:
- if self.vararg is not None:
- symlocals[self.vararg] = tuple(args)
-
- for key, val in self.kwargs:
- if key in kwargs:
- val = kwargs.pop(key)
- symlocals[key] = val
-
- if self.varkws is not None:
- symlocals[self.varkws] = kwargs
-
- elif len(kwargs) > 0:
- msg = 'extra keyword arguments for Procedure %s (%s)'
- msg = msg % (self.name, ','.join(list(kwargs.keys())))
- self.raise_exc(None, msg=msg, exc=TypeError,
- lineno=self.lineno)
-
- except (ValueError, LookupError, TypeError,
- NameError, AttributeError):
- msg = 'incorrect arguments for Procedure %s' % self.name
- self.raise_exc(None, msg=msg, lineno=self.lineno)
-
- save_symtable = self.__asteval__.symtable.copy()
- self.__asteval__.symtable.update(symlocals)
- self.__asteval__.retval = None
- retval = None
-
- # evaluate script of function
- for node in self.body:
- self.__asteval__.run(node, expr='<>', lineno=self.lineno)
- if len(self.__asteval__.error) > 0:
- break
- if self.__asteval__.retval is not None:
- retval = self.__asteval__.retval
- if retval is ReturnedNone:
- retval = None
- break
-
- self.__asteval__.symtable = save_symtable
- symlocals = None
- return retval
+"""
+Safe(ish) evaluator of python expressions, using ast module.
+The emphasis here is on mathematical expressions, and so
+numpy functions are imported if available and used.
+
+Symbols are held in the Interpreter symtable -- a simple
+dictionary supporting a simple, flat namespace.
+
+Expressions can be compiled into ast node and then evaluated
+later, using the current values in the
+"""
+
+from __future__ import division, print_function
+from sys import exc_info, stdout, version_info
+import ast
+import math
+
+from .astutils import (FROM_PY, FROM_MATH, FROM_NUMPY, UNSAFE_ATTRS,
+ LOCALFUNCS, NUMPY_RENAMES, op2func,
+ ExceptionHolder, ReturnedNone, valid_symbol_name)
+
+HAS_NUMPY = False
+try:
+ import numpy
+ HAS_NUMPY = True
+except ImportError:
+ print("Warning: numpy not available... functionality will be limited.")
+
+
+class Interpreter:
+ """mathematical expression compiler and interpreter.
+
+ This module compiles expressions and statements to AST representation,
+ using python's ast module, and then executes the AST representation
+ using a dictionary of named object (variable, functions).
+
+ The result is a restricted, simplified version of Python meant for
+ numerical caclulations that is somewhat safer than 'eval' because some
+ operations (such as 'import' and 'eval') are simply not allowed. The
+ resulting language uses a flat namespace that works on Python objects,
+ but does not allow new classes to be defined.
+
+ Many parts of Python syntax are supported, including:
+ for loops, while loops, if-then-elif-else conditionals
+ try-except (including 'finally')
+ function definitions with def
+ advanced slicing: a[::-1], array[-3:, :, ::2]
+ if-expressions: out = one_thing if TEST else other
+ list comprehension out = [sqrt(i) for i in values]
+
+ The following Python syntax elements are not supported:
+ Import, Exec, Lambda, Class, Global, Generators,
+ Yield, Decorators
+
+ In addition, while many builtin functions are supported, several
+ builtin functions are missing ('eval', 'exec', and 'getattr' for
+ example) that can be considered unsafe.
+
+ If numpy is installed, many numpy functions are also imported.
+
+ """
+
+ supported_nodes = ('arg', 'assert', 'assign', 'attribute', 'augassign',
+ 'binop', 'boolop', 'break', 'call', 'compare',
+ 'continue', 'delete', 'dict', 'ellipsis',
+ 'excepthandler', 'expr', 'extslice', 'for',
+ 'functiondef', 'if', 'ifexp', 'index', 'interrupt',
+ 'list', 'listcomp', 'module', 'name', 'num', 'pass',
+ 'print', 'raise', 'repr', 'return', 'slice', 'str',
+ 'subscript', 'try', 'tuple', 'unaryop', 'while')
+
+ def __init__(self, symtable=None, writer=None, use_numpy=True):
+ self.writer = writer or stdout
+
+ if symtable is None:
+ symtable = {}
+ self.symtable = symtable
+ self._interrupt = None
+ self.error = []
+ self.error_msg = None
+ self.expr = None
+ self.retval = None
+ self.lineno = 0
+ self.use_numpy = HAS_NUMPY and use_numpy
+
+ symtable['print'] = self._printer
+
+ # add python symbols
+ py_symtable = {sym: __builtins__[sym] for sym in FROM_PY
+ if sym in __builtins__}
+ symtable.update(py_symtable)
+
+ # add local symbols
+ local_symtable = {sym: obj for (sym, obj) in LOCALFUNCS.items()}
+ symtable.update(local_symtable)
+
+ # add math symbols
+ math_symtable = {sym: getattr(math, sym) for sym in FROM_MATH
+ if hasattr(math, sym)}
+ symtable.update(math_symtable)
+
+ # add numpy symbols
+ if self.use_numpy:
+ numpy_symtable = {sym: getattr(numpy, sym) for sym in FROM_NUMPY
+ if hasattr(numpy, sym)}
+ symtable.update(numpy_symtable)
+
+ npy_rename_symtable = {name: getattr(numpy, sym) for name, sym
+ in NUMPY_RENAMES.items()
+ if hasattr(numpy, sym)}
+ symtable.update(npy_rename_symtable)
+
+ self.node_handlers = dict(((node, getattr(self, "on_%s" % node))
+ for node in self.supported_nodes))
+
+ # to rationalize try/except try/finally for Python2.6 through Python3.3
+ self.node_handlers['tryexcept'] = self.node_handlers['try']
+ self.node_handlers['tryfinally'] = self.node_handlers['try']
+
+ self.no_deepcopy = [key for key, val in symtable.items()
+ if (callable(val)
+ or 'numpy.lib.index_tricks' in repr(val))]
+
+ def user_defined_symbols(self):
+ """
+ Return a set of symbols that have been added to symtable after
+ construction. I.e. the symbols from self.symtable that are not in
+ self.no_deepcopy.
+
+ Returns
+ -------
+ unique_symbols : set
+ symbols in symtable that are not in self.no_deepcopy
+ """
+ sym_in_current = set(self.symtable.keys())
+ sym_from_construction = set(self.no_deepcopy)
+ unique_symbols = sym_in_current.difference(sym_from_construction)
+ return unique_symbols
+
+ def unimplemented(self, node):
+ "unimplemented nodes"
+ self.raise_exception(node, exc=NotImplementedError,
+ msg="'%s' not supported" %
+ (node.__class__.__name__))
+
+ def raise_exception(self, node, exc=None, msg='', expr=None,
+ lineno=None):
+ "add an exception"
+ if self.error is None:
+ self.error = []
+ if expr is None:
+ expr = self.expr
+ if len(self.error) > 0 and not isinstance(node, ast.Module):
+ msg = '%s' % msg
+ err = ExceptionHolder(node, exc=exc, msg=msg, expr=expr, lineno=lineno)
+ self._interrupt = ast.Break()
+ self.error.append(err)
+ if self.error_msg is None:
+ self.error_msg = "%s in expr='%s'" % (msg, self.expr)
+ elif len(msg) > 0:
+ self.error_msg = "%s\n %s" % (self.error_msg, msg)
+ if exc is None:
+ try:
+ exc = self.error[0].exc
+ except:
+ exc = RuntimeError
+ raise exc(self.error_msg)
+
+
+ # main entry point for Ast node evaluation
+ # parse: text of statements -> ast
+ # run: ast -> result
+ # eval: string statement -> result = run(parse(statement))
+ def parse(self, text):
+ """parse statement/expression to Ast representation"""
+ self.expr = text
+ try:
+ return ast.parse(text)
+ except SyntaxError:
+ self.raise_exception(None, msg='Syntax Error', expr=text)
+ except:
+ self.raise_exception(None, msg='Runtime Error', expr=text)
+
+ def run(self, node, expr=None, lineno=None, with_raise=True):
+ """executes parsed Ast representation for an expression"""
+ # Note: keep the 'node is None' test: internal code here may run
+ # run(None) and expect a None in return.
+ if len(self.error) > 0:
+ return
+ if node is None:
+ return None
+ if isinstance(node, str):
+ node = self.parse(node)
+ if lineno is not None:
+ self.lineno = lineno
+ if expr is not None:
+ self.expr = expr
+
+ # get handler for this node:
+ # on_xxx with handle nodes of type 'xxx', etc
+ try:
+ handler = self.node_handlers[node.__class__.__name__.lower()]
+ except KeyError:
+ return self.unimplemented(node)
+
+ # run the handler: this will likely generate
+ # recursive calls into this run method.
+ try:
+ ret = handler(node)
+ if isinstance(ret, enumerate):
+ ret = list(ret)
+ return ret
+ except:
+ if with_raise:
+ self.raise_exception(node, expr=expr)
+
+ def __call__(self, expr, **kw):
+ return self.eval(expr, **kw)
+
+ def eval(self, expr, lineno=0, show_errors=True):
+ """evaluates a single statement"""
+ self.lineno = lineno
+ self.error = []
+ try:
+ node = self.parse(expr)
+ except:
+ errmsg = exc_info()[1]
+ if len(self.error) > 0:
+ errmsg = "\n".join(self.error[0].get_error())
+ if not show_errors:
+ try:
+ exc = self.error[0].exc
+ except:
+ exc = RuntimeError
+ raise exc(errmsg)
+ print(errmsg, file=self.writer)
+ return
+ try:
+ return self.run(node, expr=expr, lineno=lineno)
+ except:
+ errmsg = exc_info()[1]
+ if len(self.error) > 0:
+ errmsg = "\n".join(self.error[0].get_error())
+ if not show_errors:
+ try:
+ exc = self.error[0].exc
+ except:
+ exc = RuntimeError
+ raise exc(errmsg)
+ print(errmsg, file=self.writer)
+ return
+
+ def dump(self, node, **kw):
+ "simple ast dumper"
+ return ast.dump(node, **kw)
+
+ # handlers for ast components
+ def on_expr(self, node):
+ "expression"
+ return self.run(node.value) # ('value',)
+
+ def on_index(self, node):
+ "index"
+ return self.run(node.value) # ('value',)
+
+ def on_return(self, node): # ('value',)
+ "return statement: look for None, return special sentinal"
+ self.retval = self.run(node.value)
+ if self.retval is None:
+ self.retval = ReturnedNone
+ return
+
+ def on_repr(self, node):
+ "repr "
+ return repr(self.run(node.value)) # ('value',)
+
+ def on_module(self, node): # ():('body',)
+ "module def"
+ out = None
+ for tnode in node.body:
+ out = self.run(tnode)
+ return out
+
+ def on_pass(self, node):
+ "pass statement"
+ return None # ()
+
+ def on_ellipsis(self, node):
+ "ellipses"
+ return Ellipsis
+
+ # for break and continue: set the instance variable _interrupt
+ def on_interrupt(self, node): # ()
+ "interrupt handler"
+ self._interrupt = node
+ return node
+
+ def on_break(self, node):
+ "break"
+ return self.on_interrupt(node)
+
+ def on_continue(self, node):
+ "continue"
+ return self.on_interrupt(node)
+
+ def on_assert(self, node): # ('test', 'msg')
+ "assert statement"
+ if not self.run(node.test):
+ self.raise_exception(node, exc=AssertionError, msg=node.msg)
+ return True
+
+ def on_list(self, node): # ('elt', 'ctx')
+ "list"
+ return [self.run(e) for e in node.elts]
+
+ def on_tuple(self, node): # ('elts', 'ctx')
+ "tuple"
+ return tuple(self.on_list(node))
+
+ def on_dict(self, node): # ('keys', 'values')
+ "dictionary"
+ return dict([(self.run(k), self.run(v)) for k, v in
+ zip(node.keys, node.values)])
+
+ def on_num(self, node): # ('n',)
+ 'return number'
+ return node.n
+
+ def on_str(self, node): # ('s',)
+ 'return string'
+ return node.s
+
+ def on_name(self, node): # ('id', 'ctx')
+ """ Name node """
+ ctx = node.ctx.__class__
+ if ctx in (ast.Param, ast.Del):
+ return str(node.id)
+ else:
+ if node.id in self.symtable:
+ return self.symtable[node.id]
+ else:
+ msg = "name '%s' is not defined" % node.id
+ self.raise_exception(node, exc=NameError, msg=msg)
+
+ def node_assign(self, node, val):
+ """here we assign a value (not the node.value object) to a node
+ this is used by on_assign, but also by for, list comprehension, etc.
+ """
+ if node.__class__ == ast.Name:
+ if not valid_symbol_name(node.id):
+ errmsg = "invalid symbol name (reserved word?) %s" % node.id
+ self.raise_exception(node, exc=NameError, msg=errmsg)
+ sym = self.symtable[node.id] = val
+ if node.id in self.no_deepcopy:
+ self.no_deepcopy.pop(node.id)
+
+ elif node.__class__ == ast.Attribute:
+ if node.ctx.__class__ == ast.Load:
+ msg = "cannot assign to attribute %s" % node.attr
+ self.raise_exception(node, exc=AttributeError, msg=msg)
+
+ setattr(self.run(node.value), node.attr, val)
+
+ elif node.__class__ == ast.Subscript:
+ sym = self.run(node.value)
+ xslice = self.run(node.slice)
+ if isinstance(node.slice, ast.Index):
+ sym[xslice] = val
+ elif isinstance(node.slice, ast.Slice):
+ sym[slice(xslice.start, xslice.stop)] = val
+ elif isinstance(node.slice, ast.ExtSlice):
+ sym[(xslice)] = val
+ elif node.__class__ in (ast.Tuple, ast.List):
+ if len(val) == len(node.elts):
+ for telem, tval in zip(node.elts, val):
+ self.node_assign(telem, tval)
+ else:
+ raise ValueError('too many values to unpack')
+
+ def on_attribute(self, node): # ('value', 'attr', 'ctx')
+ "extract attribute"
+ ctx = node.ctx.__class__
+ if ctx == ast.Store:
+ msg = "attribute for storage: shouldn't be here!"
+ self.raise_exception(node, exc=RuntimeError, msg=msg)
+
+ sym = self.run(node.value)
+ if ctx == ast.Del:
+ return delattr(sym, node.attr)
+
+ # ctx is ast.Load
+ fmt = "cannnot access attribute '%s' for %s"
+ if node.attr not in UNSAFE_ATTRS:
+ fmt = "no attribute '%s' for %s"
+ try:
+ return getattr(sym, node.attr)
+ except AttributeError:
+ pass
+
+ # AttributeError or accessed unsafe attribute
+ obj = self.run(node.value)
+ msg = fmt % (node.attr, obj)
+ self.raise_exception(node, exc=AttributeError, msg=msg)
+
+ def on_assign(self, node): # ('targets', 'value')
+ "simple assignment"
+ val = self.run(node.value)
+ for tnode in node.targets:
+ self.node_assign(tnode, val)
+ return
+
+ def on_augassign(self, node): # ('target', 'op', 'value')
+ "augmented assign"
+ return self.on_assign(ast.Assign(targets=[node.target],
+ value=ast.BinOp(left=node.target,
+ op=node.op,
+ right=node.value)))
+
+ def on_slice(self, node): # ():('lower', 'upper', 'step')
+ "simple slice"
+ return slice(self.run(node.lower),
+ self.run(node.upper),
+ self.run(node.step))
+
+ def on_extslice(self, node): # ():('dims',)
+ "extended slice"
+ return tuple([self.run(tnode) for tnode in node.dims])
+
+ def on_subscript(self, node): # ('value', 'slice', 'ctx')
+ "subscript handling -- one of the tricky parts"
+ val = self.run(node.value)
+ nslice = self.run(node.slice)
+ ctx = node.ctx.__class__
+ if ctx in (ast.Load, ast.Store):
+ if isinstance(node.slice, (ast.Index, ast.Slice, ast.Ellipsis)):
+ return val.__getitem__(nslice)
+ elif isinstance(node.slice, ast.ExtSlice):
+ return val[(nslice)]
+ else:
+ msg = "subscript with unknown context"
+ self.raise_exception(node, msg=msg)
+
+ def on_delete(self, node): # ('targets',)
+ "delete statement"
+ for tnode in node.targets:
+ if tnode.ctx.__class__ != ast.Del:
+ break
+ children = []
+ while tnode.__class__ == ast.Attribute:
+ children.append(tnode.attr)
+ tnode = tnode.value
+
+ if tnode.__class__ == ast.Name:
+ children.append(tnode.id)
+ children.reverse()
+ self.symtable.pop('.'.join(children))
+ else:
+ msg = "could not delete symbol"
+ self.raise_exception(node, msg=msg)
+
+ def on_unaryop(self, node): # ('op', 'operand')
+ "unary operator"
+ return op2func(node.op)(self.run(node.operand))
+
+ def on_binop(self, node): # ('left', 'op', 'right')
+ "binary operator"
+ return op2func(node.op)(self.run(node.left),
+ self.run(node.right))
+
+ def on_boolop(self, node): # ('op', 'values')
+ "boolean operator"
+ val = self.run(node.values[0])
+ is_and = ast.And == node.op.__class__
+ if (is_and and val) or (not is_and and not val):
+ for n in node.values:
+ val = op2func(node.op)(val, self.run(n))
+ if (is_and and not val) or (not is_and and val):
+ break
+ return val
+
+ def on_compare(self, node): # ('left', 'ops', 'comparators')
+ "comparison operators"
+ lval = self.run(node.left)
+ out = True
+ for op, rnode in zip(node.ops, node.comparators):
+ rval = self.run(rnode)
+ out = op2func(op)(lval, rval)
+ lval = rval
+ if self.use_numpy and isinstance(out, numpy.ndarray) and out.any():
+ break
+ elif not out:
+ break
+ return out
+
+ def on_print(self, node): # ('dest', 'values', 'nl')
+ """ note: implements Python2 style print statement, not
+ print() function. May need improvement...."""
+ dest = self.run(node.dest) or self.writer
+ end = ''
+ if node.nl:
+ end = '\n'
+ out = [self.run(tnode) for tnode in node.values]
+ if out and len(self.error) == 0:
+ self._printer(*out, file=dest, end=end)
+
+ def _printer(self, *out, **kws):
+ "generic print function"
+ flush = kws.pop('flush', True)
+ fileh = kws.pop('file', self.writer)
+ sep = kws.pop('sep', ' ')
+ end = kws.pop('sep', '\n')
+
+ print(*out, file=fileh, sep=sep, end=end)
+ if flush:
+ fileh.flush()
+
+ def on_if(self, node): # ('test', 'body', 'orelse')
+ "regular if-then-else statement"
+ block = node.body
+ if not self.run(node.test):
+ block = node.orelse
+ for tnode in block:
+ self.run(tnode)
+
+ def on_ifexp(self, node): # ('test', 'body', 'orelse')
+ "if expressions"
+ expr = node.orelse
+ if self.run(node.test):
+ expr = node.body
+ return self.run(expr)
+
+ def on_while(self, node): # ('test', 'body', 'orelse')
+ "while blocks"
+ while self.run(node.test):
+ self._interrupt = None
+ for tnode in node.body:
+ self.run(tnode)
+ if self._interrupt is not None:
+ break
+ if isinstance(self._interrupt, ast.Break):
+ break
+ else:
+ for tnode in node.orelse:
+ self.run(tnode)
+ self._interrupt = None
+
+ def on_for(self, node): # ('target', 'iter', 'body', 'orelse')
+ "for blocks"
+ for val in self.run(node.iter):
+ self.node_assign(node.target, val)
+ self._interrupt = None
+ for tnode in node.body:
+ self.run(tnode)
+ if self._interrupt is not None:
+ break
+ if isinstance(self._interrupt, ast.Break):
+ break
+ else:
+ for tnode in node.orelse:
+ self.run(tnode)
+ self._interrupt = None
+
+ def on_listcomp(self, node): # ('elt', 'generators')
+ "list comprehension"
+ out = []
+ for tnode in node.generators:
+ if tnode.__class__ == ast.comprehension:
+ for val in self.run(tnode.iter):
+ self.node_assign(tnode.target, val)
+ add = True
+ for cond in tnode.ifs:
+ add = add and self.run(cond)
+ if add:
+ out.append(self.run(node.elt))
+ return out
+
+ def on_excepthandler(self, node): # ('type', 'name', 'body')
+ "exception handler..."
+ return (self.run(node.type), node.name, node.body)
+
+ def on_try(self, node): # ('body', 'handlers', 'orelse', 'finalbody')
+ "try/except/else/finally blocks"
+ no_errors = True
+ for tnode in node.body:
+ self.run(tnode, with_raise=False)
+ no_errors = no_errors and len(self.error) == 0
+ if len(self.error) > 0:
+ e_type, e_value, e_tback = self.error[-1].exc_info
+ for hnd in node.handlers:
+ htype = None
+ if hnd.type is not None:
+ htype = __builtins__.get(hnd.type.id, None)
+ if htype is None or isinstance(e_type(), htype):
+ self.error = []
+ if hnd.name is not None:
+ self.node_assign(hnd.name, e_value)
+ for tline in hnd.body:
+ self.run(tline)
+ break
+ if no_errors and hasattr(node, 'orelse'):
+ for tnode in node.orelse:
+ self.run(tnode)
+
+ if hasattr(node, 'finalbody'):
+ for tnode in node.finalbody:
+ self.run(tnode)
+
+ def on_raise(self, node): # ('type', 'inst', 'tback')
+ "raise statement: note difference for python 2 and 3"
+ if version_info[0] == 3:
+ excnode = node.exc
+ msgnode = node.cause
+ else:
+ excnode = node.type
+ msgnode = node.inst
+ out = self.run(excnode)
+ msg = ' '.join(out.args)
+ msg2 = self.run(msgnode)
+ if msg2 not in (None, 'None'):
+ msg = "%s: %s" % (msg, msg2)
+ self.raise_exception(None, exc=out.__class__, msg=msg, expr='')
+
+ def on_call(self, node):
+ "function execution"
+ # ('func', 'args', 'keywords'. Py<3.5 has 'starargs' and 'kwargs' too)
+ func = self.run(node.func)
+ if not hasattr(func, '__call__') and not isinstance(func, type):
+ msg = "'%s' is not callable!!" % (func)
+ self.raise_exception(node, exc=TypeError, msg=msg)
+
+ args = [self.run(targ) for targ in node.args]
+ starargs = getattr(node, 'starargs', None)
+ if starargs is not None:
+ args = args + self.run(starargs)
+
+ keywords = {}
+ for key in node.keywords:
+ if not isinstance(key, ast.keyword):
+ msg = "keyword error in function call '%s'" % (func)
+ self.raise_exception(node, msg=msg)
+ keywords[key.arg] = self.run(key.value)
+
+ kwargs = getattr(node, 'kwargs', None)
+ if kwargs is not None:
+ keywords.update(self.run(kwargs))
+
+ try:
+ return func(*args, **keywords)
+ except:
+ self.raise_exception(node, msg="Error running %s" % (func))
+
+ def on_arg(self, node): # ('test', 'msg')
+ "arg for function definitions"
+ # print(" ON ARG ! ", node, node.arg)
+ return node.arg
+
+ def on_functiondef(self, node):
+ "define procedures"
+ # ('name', 'args', 'body', 'decorator_list')
+ if node.decorator_list != []:
+ raise Warning("decorated procedures not supported!")
+ kwargs = []
+
+ offset = len(node.args.args) - len(node.args.defaults)
+ for idef, defnode in enumerate(node.args.defaults):
+ defval = self.run(defnode)
+ keyval = self.run(node.args.args[idef+offset])
+ kwargs.append((keyval, defval))
+
+ if version_info[0] == 3:
+ args = [tnode.arg for tnode in node.args.args[:offset]]
+ else:
+ args = [tnode.id for tnode in node.args.args[:offset]]
+
+ doc = None
+ nb0 = node.body[0]
+ if isinstance(nb0, ast.Expr) and isinstance(nb0.value, ast.Str):
+ doc = nb0.value.s
+
+ self.symtable[node.name] = Procedure(node.name, self, doc=doc,
+ lineno=self.lineno,
+ body=node.body,
+ args=args, kwargs=kwargs,
+ vararg=node.args.vararg,
+ varkws=node.args.kwarg)
+ if node.name in self.no_deepcopy:
+ self.no_deepcopy.pop(node.name)
+
+
+class Procedure(object):
+ """Procedure: user-defined function for asteval
+
+ This stores the parsed ast nodes as from the
+ 'functiondef' ast node for later evaluation.
+ """
+ def __init__(self, name, interp, doc=None, lineno=0,
+ body=None, args=None, kwargs=None,
+ vararg=None, varkws=None):
+ self.name = name
+ self.__asteval__ = interp
+ self.raise_exc = self.__asteval__.raise_exception
+ self.__doc__ = doc
+ self.body = body
+ self.argnames = args
+ self.kwargs = kwargs
+ self.vararg = vararg
+ self.varkws = varkws
+ self.lineno = lineno
+
+ def __repr__(self):
+ sig = ""
+ if len(self.argnames) > 0:
+ sig = "%s%s" % (sig, ', '.join(self.argnames))
+ if self.vararg is not None:
+ sig = "%s, *%s" % (sig, self.vararg)
+ if len(self.kwargs) > 0:
+ if len(sig) > 0:
+ sig = "%s, " % sig
+ _kw = ["%s=%s" % (k, v) for k, v in self.kwargs]
+ sig = "%s%s" % (sig, ', '.join(_kw))
+
+ if self.varkws is not None:
+ sig = "%s, **%s" % (sig, self.varkws)
+ sig = "<Procedure %s(%s)>" % (self.name, sig)
+ if self.__doc__ is not None:
+ sig = "%s\n %s" % (sig, self.__doc__)
+ return sig
+
+ def __call__(self, *args, **kwargs):
+ symlocals = {}
+ args = list(args)
+ n_args = len(args)
+ n_names = len(self.argnames)
+ n_kws = len(kwargs)
+
+ # may need to move kwargs to args if names align!
+ if (n_args < n_names) and n_kws > 0:
+ for name in self.argnames[n_args:]:
+ if name in kwargs:
+ args.append(kwargs.pop(name))
+ n_args = len(args)
+ n_names = len(self.argnames)
+ n_kws = len(kwargs)
+
+ if len(self.argnames) > 0 and kwargs is not None:
+ msg = "multiple values for keyword argument '%s' in Procedure %s"
+ for targ in self.argnames:
+ if targ in kwargs:
+ self.raise_exc(None, exc=TypeError,
+ msg=msg % (targ, self.name),
+ lineno=self.lineno)
+
+ if n_args != n_names:
+ msg = None
+ if n_args < n_names:
+ msg = 'not enough arguments for Procedure %s()' % self.name
+ msg = '%s (expected %i, got %i)' % (msg, n_names, n_args)
+ self.raise_exc(None, exc=TypeError, msg=msg)
+
+ for argname in self.argnames:
+ symlocals[argname] = args.pop(0)
+
+ try:
+ if self.vararg is not None:
+ symlocals[self.vararg] = tuple(args)
+
+ for key, val in self.kwargs:
+ if key in kwargs:
+ val = kwargs.pop(key)
+ symlocals[key] = val
+
+ if self.varkws is not None:
+ symlocals[self.varkws] = kwargs
+
+ elif len(kwargs) > 0:
+ msg = 'extra keyword arguments for Procedure %s (%s)'
+ msg = msg % (self.name, ','.join(list(kwargs.keys())))
+ self.raise_exc(None, msg=msg, exc=TypeError,
+ lineno=self.lineno)
+
+ except (ValueError, LookupError, TypeError,
+ NameError, AttributeError):
+ msg = 'incorrect arguments for Procedure %s' % self.name
+ self.raise_exc(None, msg=msg, lineno=self.lineno)
+
+ save_symtable = self.__asteval__.symtable.copy()
+ self.__asteval__.symtable.update(symlocals)
+ self.__asteval__.retval = None
+ retval = None
+
+ # evaluate script of function
+ for node in self.body:
+ self.__asteval__.run(node, expr='<>', lineno=self.lineno)
+ if len(self.__asteval__.error) > 0:
+ break
+ if self.__asteval__.retval is not None:
+ retval = self.__asteval__.retval
+ if retval is ReturnedNone:
+ retval = None
+ break
+
+ self.__asteval__.symtable = save_symtable
+ symlocals = None
+ return retval
diff --git a/lmfit/astutils.py b/lmfit/astutils.py
index 0a8c25a..9df7146 100644
--- a/lmfit/astutils.py
+++ b/lmfit/astutils.py
@@ -1,258 +1,258 @@
-"""
-utility functions for asteval
-
- Matthew Newville <newville at cars.uchicago.edu>,
- The University of Chicago
-"""
-from __future__ import division, print_function
-import re
-import ast
-from sys import exc_info
-
-RESERVED_WORDS = ('and', 'as', 'assert', 'break', 'class', 'continue',
- 'def', 'del', 'elif', 'else', 'except', 'exec',
- 'finally', 'for', 'from', 'global', 'if', 'import',
- 'in', 'is', 'lambda', 'not', 'or', 'pass', 'print',
- 'raise', 'return', 'try', 'while', 'with', 'True',
- 'False', 'None', 'eval', 'execfile', '__import__',
- '__package__')
-
-NAME_MATCH = re.compile(r"[a-zA-Z_][a-zA-Z0-9_]*$").match
-
-UNSAFE_ATTRS = ('__subclasses__', '__bases__', '__globals__', '__code__',
- '__closure__', '__func__', '__self__', '__module__',
- '__dict__', '__class__', '__call__', '__get__',
- '__getattribute__', '__subclasshook__', '__new__',
- '__init__', 'func_globals', 'func_code', 'func_closure',
- 'im_class', 'im_func', 'im_self', 'gi_code', 'gi_frame',
- '__asteval__')
-
-# inherit these from python's __builtins__
-FROM_PY = ('ArithmeticError', 'AssertionError', 'AttributeError',
- 'BaseException', 'BufferError', 'BytesWarning',
- 'DeprecationWarning', 'EOFError', 'EnvironmentError',
- 'Exception', 'False', 'FloatingPointError', 'GeneratorExit',
- 'IOError', 'ImportError', 'ImportWarning', 'IndentationError',
- 'IndexError', 'KeyError', 'KeyboardInterrupt', 'LookupError',
- 'MemoryError', 'NameError', 'None',
- 'NotImplementedError', 'OSError', 'OverflowError',
- 'ReferenceError', 'RuntimeError', 'RuntimeWarning',
- 'StopIteration', 'SyntaxError', 'SyntaxWarning', 'SystemError',
- 'SystemExit', 'True', 'TypeError', 'UnboundLocalError',
- 'UnicodeDecodeError', 'UnicodeEncodeError', 'UnicodeError',
- 'UnicodeTranslateError', 'UnicodeWarning', 'ValueError',
- 'Warning', 'ZeroDivisionError', 'abs', 'all', 'any', 'bin',
- 'bool', 'bytearray', 'bytes', 'chr', 'complex', 'dict', 'dir',
- 'divmod', 'enumerate', 'filter', 'float', 'format', 'frozenset',
- 'hash', 'hex', 'id', 'int', 'isinstance', 'len', 'list', 'map',
- 'max', 'min', 'oct', 'ord', 'pow', 'range', 'repr',
- 'reversed', 'round', 'set', 'slice', 'sorted', 'str', 'sum',
- 'tuple', 'type', 'zip')
-
-# inherit these from python's math
-FROM_MATH = ('acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2', 'atanh',
- 'ceil', 'copysign', 'cos', 'cosh', 'degrees', 'e', 'exp',
- 'fabs', 'factorial', 'floor', 'fmod', 'frexp', 'fsum',
- 'hypot', 'isinf', 'isnan', 'ldexp', 'log', 'log10', 'log1p',
- 'modf', 'pi', 'pow', 'radians', 'sin', 'sinh', 'sqrt', 'tan',
- 'tanh', 'trunc')
-
-FROM_NUMPY = ('Inf', 'NAN', 'abs', 'add', 'alen', 'all', 'amax', 'amin',
- 'angle', 'any', 'append', 'arange', 'arccos', 'arccosh',
- 'arcsin', 'arcsinh', 'arctan', 'arctan2', 'arctanh',
- 'argmax', 'argmin', 'argsort', 'argwhere', 'around', 'array',
- 'array2string', 'asanyarray', 'asarray', 'asarray_chkfinite',
- 'ascontiguousarray', 'asfarray', 'asfortranarray',
- 'asmatrix', 'asscalar', 'atleast_1d', 'atleast_2d',
- 'atleast_3d', 'average', 'bartlett', 'base_repr',
- 'bitwise_and', 'bitwise_not', 'bitwise_or', 'bitwise_xor',
- 'blackman', 'bool', 'broadcast', 'broadcast_arrays', 'byte',
- 'c_', 'cdouble', 'ceil', 'cfloat', 'chararray', 'choose',
- 'clip', 'clongdouble', 'clongfloat', 'column_stack',
- 'common_type', 'complex', 'complex128', 'complex64',
- 'complex_', 'complexfloating', 'compress', 'concatenate',
- 'conjugate', 'convolve', 'copy', 'copysign', 'corrcoef',
- 'correlate', 'cos', 'cosh', 'cov', 'cross', 'csingle',
- 'cumprod', 'cumsum', 'datetime_data', 'deg2rad', 'degrees',
- 'delete', 'diag', 'diag_indices', 'diag_indices_from',
- 'diagflat', 'diagonal', 'diff', 'digitize', 'divide', 'dot',
- 'double', 'dsplit', 'dstack', 'dtype', 'e', 'ediff1d',
- 'empty', 'empty_like', 'equal', 'exp', 'exp2', 'expand_dims',
- 'expm1', 'extract', 'eye', 'fabs', 'fill_diagonal', 'finfo',
- 'fix', 'flatiter', 'flatnonzero', 'fliplr', 'flipud',
- 'float', 'float32', 'float64', 'float_', 'floating', 'floor',
- 'floor_divide', 'fmax', 'fmin', 'fmod', 'format_parser',
- 'frexp', 'frombuffer', 'fromfile', 'fromfunction',
- 'fromiter', 'frompyfunc', 'fromregex', 'fromstring', 'fv',
- 'genfromtxt', 'getbufsize', 'geterr', 'gradient', 'greater',
- 'greater_equal', 'hamming', 'hanning', 'histogram',
- 'histogram2d', 'histogramdd', 'hsplit', 'hstack', 'hypot',
- 'i0', 'identity', 'iinfo', 'imag', 'in1d', 'index_exp',
- 'indices', 'inexact', 'inf', 'info', 'infty', 'inner',
- 'insert', 'int', 'int0', 'int16', 'int32', 'int64', 'int8',
- 'int_', 'int_asbuffer', 'intc', 'integer', 'interp',
- 'intersect1d', 'intp', 'invert', 'ipmt', 'irr', 'iscomplex',
- 'iscomplexobj', 'isfinite', 'isfortran', 'isinf', 'isnan',
- 'isneginf', 'isposinf', 'isreal', 'isrealobj', 'isscalar',
- 'issctype', 'iterable', 'ix_', 'kaiser', 'kron', 'ldexp',
- 'left_shift', 'less', 'less_equal', 'linspace',
- 'little_endian', 'load', 'loads', 'loadtxt', 'log', 'log10',
- 'log1p', 'log2', 'logaddexp', 'logaddexp2', 'logical_and',
- 'logical_not', 'logical_or', 'logical_xor', 'logspace',
- 'long', 'longcomplex', 'longdouble', 'longfloat', 'longlong',
- 'mafromtxt', 'mask_indices', 'mat', 'matrix', 'max',
- 'maximum', 'maximum_sctype', 'may_share_memory', 'mean',
- 'median', 'memmap', 'meshgrid', 'mgrid', 'min', 'minimum',
- 'mintypecode', 'mirr', 'mod', 'modf', 'msort', 'multiply',
- 'nan', 'nan_to_num', 'nanargmax', 'nanargmin', 'nanmax',
- 'nanmin', 'nansum', 'ndarray', 'ndenumerate', 'ndfromtxt',
- 'ndim', 'ndindex', 'negative', 'newaxis', 'nextafter',
- 'nonzero', 'not_equal', 'nper', 'npv', 'number',
- 'obj2sctype', 'ogrid', 'ones', 'ones_like', 'outer',
- 'packbits', 'percentile', 'pi', 'piecewise', 'place', 'pmt',
- 'poly', 'poly1d', 'polyadd', 'polyder', 'polydiv', 'polyfit',
- 'polyint', 'polymul', 'polysub', 'polyval', 'power', 'ppmt',
- 'prod', 'product', 'ptp', 'put', 'putmask', 'pv', 'r_',
- 'rad2deg', 'radians', 'rank', 'rate', 'ravel', 'real',
- 'real_if_close', 'reciprocal', 'record', 'remainder',
- 'repeat', 'reshape', 'resize', 'restoredot', 'right_shift',
- 'rint', 'roll', 'rollaxis', 'roots', 'rot90', 'round',
- 'round_', 'row_stack', 's_', 'sctype2char', 'searchsorted',
- 'select', 'setbufsize', 'setdiff1d', 'seterr', 'setxor1d',
- 'shape', 'short', 'sign', 'signbit', 'signedinteger', 'sin',
- 'sinc', 'single', 'singlecomplex', 'sinh', 'size',
- 'sometrue', 'sort', 'sort_complex', 'spacing', 'split',
- 'sqrt', 'square', 'squeeze', 'std', 'str', 'str_',
- 'subtract', 'sum', 'swapaxes', 'take', 'tan', 'tanh',
- 'tensordot', 'tile', 'trace', 'transpose', 'trapz', 'tri',
- 'tril', 'tril_indices', 'tril_indices_from', 'trim_zeros',
- 'triu', 'triu_indices', 'triu_indices_from', 'true_divide',
- 'trunc', 'ubyte', 'uint', 'uint0', 'uint16', 'uint32',
- 'uint64', 'uint8', 'uintc', 'uintp', 'ulonglong', 'union1d',
- 'unique', 'unravel_index', 'unsignedinteger', 'unwrap',
- 'ushort', 'vander', 'var', 'vdot', 'vectorize', 'vsplit',
- 'vstack', 'where', 'who', 'zeros', 'zeros_like')
-
-NUMPY_RENAMES = {'ln': 'log', 'asin': 'arcsin', 'acos': 'arccos',
- 'atan': 'arctan', 'atan2': 'arctan2', 'atanh':
- 'arctanh', 'acosh': 'arccosh', 'asinh': 'arcsinh'}
-
-def _open(filename, mode='r', buffering=0):
- """read only version of open()"""
- umode = 'r'
- if mode == 'rb':
- umode = 'rb'
- return open(filename, umode, buffering)
-
-LOCALFUNCS = {'open': _open}
-
-OPERATORS = {ast.Is: lambda a, b: a is b,
- ast.IsNot: lambda a, b: a is not b,
- ast.In: lambda a, b: a in b,
- ast.NotIn: lambda a, b: a not in b,
- ast.Add: lambda a, b: a + b,
- ast.BitAnd: lambda a, b: a & b,
- ast.BitOr: lambda a, b: a | b,
- ast.BitXor: lambda a, b: a ^ b,
- ast.Div: lambda a, b: a / b,
- ast.FloorDiv: lambda a, b: a // b,
- ast.LShift: lambda a, b: a << b,
- ast.RShift: lambda a, b: a >> b,
- ast.Mult: lambda a, b: a * b,
- ast.Pow: lambda a, b: a ** b,
- ast.Sub: lambda a, b: a - b,
- ast.Mod: lambda a, b: a % b,
- ast.And: lambda a, b: a and b,
- ast.Or: lambda a, b: a or b,
- ast.Eq: lambda a, b: a == b,
- ast.Gt: lambda a, b: a > b,
- ast.GtE: lambda a, b: a >= b,
- ast.Lt: lambda a, b: a < b,
- ast.LtE: lambda a, b: a <= b,
- ast.NotEq: lambda a, b: a != b,
- ast.Invert: lambda a: ~a,
- ast.Not: lambda a: not a,
- ast.UAdd: lambda a: +a,
- ast.USub: lambda a: -a}
-
-
-def valid_symbol_name(name):
- """determines whether the input symbol name is a valid name
-
- This checks for reserved words, and that the name matches the
- regular expression ``[a-zA-Z_][a-zA-Z0-9_]``
- """
- if name in RESERVED_WORDS:
- return False
- return NAME_MATCH(name) is not None
-
-
-def op2func(op):
- "return function for operator nodes"
- return OPERATORS[op.__class__]
-
-
-class Empty:
- """empty class"""
- def __init__(self):
- pass
-
- def __nonzero__(self):
- return False
-
-ReturnedNone = Empty()
-
-
-class ExceptionHolder(object):
- "basic exception handler"
- def __init__(self, node, exc=None, msg='', expr=None, lineno=None):
- self.node = node
- self.expr = expr
- self.msg = msg
- self.exc = exc
- self.lineno = lineno
- self.exc_info = exc_info()
- if self.exc is None and self.exc_info[0] is not None:
- self.exc = self.exc_info[0]
- if self.msg is '' and self.exc_info[1] is not None:
- self.msg = self.exc_info[1]
-
- def get_error(self):
- "retrieve error data"
- col_offset = -1
- if self.node is not None:
- try:
- col_offset = self.node.col_offset
- except AttributeError:
- pass
- try:
- exc_name = self.exc.__name__
- except AttributeError:
- exc_name = str(self.exc)
- if exc_name in (None, 'None'):
- exc_name = 'UnknownError'
-
- out = [" %s" % self.expr]
- if col_offset > 0:
- out.append(" %s^^^" % ((col_offset)*' '))
- out.append(str(self.msg))
- return (exc_name, '\n'.join(out))
-
-
-class NameFinder(ast.NodeVisitor):
- """find all symbol names used by a parsed node"""
- def __init__(self):
- self.names = []
- ast.NodeVisitor.__init__(self)
-
- def generic_visit(self, node):
- if node.__class__.__name__ == 'Name':
- if node.ctx.__class__ == ast.Load and node.id not in self.names:
- self.names.append(node.id)
- ast.NodeVisitor.generic_visit(self, node)
-
-def get_ast_names(astnode):
- "returns symbol Names from an AST node"
- finder = NameFinder()
- finder.generic_visit(astnode)
- return finder.names
+"""
+utility functions for asteval
+
+ Matthew Newville <newville at cars.uchicago.edu>,
+ The University of Chicago
+"""
+from __future__ import division, print_function
+import re
+import ast
+from sys import exc_info
+
+RESERVED_WORDS = ('and', 'as', 'assert', 'break', 'class', 'continue',
+ 'def', 'del', 'elif', 'else', 'except', 'exec',
+ 'finally', 'for', 'from', 'global', 'if', 'import',
+ 'in', 'is', 'lambda', 'not', 'or', 'pass', 'print',
+ 'raise', 'return', 'try', 'while', 'with', 'True',
+ 'False', 'None', 'eval', 'execfile', '__import__',
+ '__package__')
+
+NAME_MATCH = re.compile(r"[a-zA-Z_][a-zA-Z0-9_]*$").match
+
+UNSAFE_ATTRS = ('__subclasses__', '__bases__', '__globals__', '__code__',
+ '__closure__', '__func__', '__self__', '__module__',
+ '__dict__', '__class__', '__call__', '__get__',
+ '__getattribute__', '__subclasshook__', '__new__',
+ '__init__', 'func_globals', 'func_code', 'func_closure',
+ 'im_class', 'im_func', 'im_self', 'gi_code', 'gi_frame',
+ '__asteval__')
+
+# inherit these from python's __builtins__
+FROM_PY = ('ArithmeticError', 'AssertionError', 'AttributeError',
+ 'BaseException', 'BufferError', 'BytesWarning',
+ 'DeprecationWarning', 'EOFError', 'EnvironmentError',
+ 'Exception', 'False', 'FloatingPointError', 'GeneratorExit',
+ 'IOError', 'ImportError', 'ImportWarning', 'IndentationError',
+ 'IndexError', 'KeyError', 'KeyboardInterrupt', 'LookupError',
+ 'MemoryError', 'NameError', 'None',
+ 'NotImplementedError', 'OSError', 'OverflowError',
+ 'ReferenceError', 'RuntimeError', 'RuntimeWarning',
+ 'StopIteration', 'SyntaxError', 'SyntaxWarning', 'SystemError',
+ 'SystemExit', 'True', 'TypeError', 'UnboundLocalError',
+ 'UnicodeDecodeError', 'UnicodeEncodeError', 'UnicodeError',
+ 'UnicodeTranslateError', 'UnicodeWarning', 'ValueError',
+ 'Warning', 'ZeroDivisionError', 'abs', 'all', 'any', 'bin',
+ 'bool', 'bytearray', 'bytes', 'chr', 'complex', 'dict', 'dir',
+ 'divmod', 'enumerate', 'filter', 'float', 'format', 'frozenset',
+ 'hash', 'hex', 'id', 'int', 'isinstance', 'len', 'list', 'map',
+ 'max', 'min', 'oct', 'ord', 'pow', 'range', 'repr',
+ 'reversed', 'round', 'set', 'slice', 'sorted', 'str', 'sum',
+ 'tuple', 'type', 'zip')
+
+# inherit these from python's math
+FROM_MATH = ('acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2', 'atanh',
+ 'ceil', 'copysign', 'cos', 'cosh', 'degrees', 'e', 'exp',
+ 'fabs', 'factorial', 'floor', 'fmod', 'frexp', 'fsum',
+ 'hypot', 'isinf', 'isnan', 'ldexp', 'log', 'log10', 'log1p',
+ 'modf', 'pi', 'pow', 'radians', 'sin', 'sinh', 'sqrt', 'tan',
+ 'tanh', 'trunc')
+
+FROM_NUMPY = ('Inf', 'NAN', 'abs', 'add', 'alen', 'all', 'amax', 'amin',
+ 'angle', 'any', 'append', 'arange', 'arccos', 'arccosh',
+ 'arcsin', 'arcsinh', 'arctan', 'arctan2', 'arctanh',
+ 'argmax', 'argmin', 'argsort', 'argwhere', 'around', 'array',
+ 'array2string', 'asanyarray', 'asarray', 'asarray_chkfinite',
+ 'ascontiguousarray', 'asfarray', 'asfortranarray',
+ 'asmatrix', 'asscalar', 'atleast_1d', 'atleast_2d',
+ 'atleast_3d', 'average', 'bartlett', 'base_repr',
+ 'bitwise_and', 'bitwise_not', 'bitwise_or', 'bitwise_xor',
+ 'blackman', 'bool', 'broadcast', 'broadcast_arrays', 'byte',
+ 'c_', 'cdouble', 'ceil', 'cfloat', 'chararray', 'choose',
+ 'clip', 'clongdouble', 'clongfloat', 'column_stack',
+ 'common_type', 'complex', 'complex128', 'complex64',
+ 'complex_', 'complexfloating', 'compress', 'concatenate',
+ 'conjugate', 'convolve', 'copy', 'copysign', 'corrcoef',
+ 'correlate', 'cos', 'cosh', 'cov', 'cross', 'csingle',
+ 'cumprod', 'cumsum', 'datetime_data', 'deg2rad', 'degrees',
+ 'delete', 'diag', 'diag_indices', 'diag_indices_from',
+ 'diagflat', 'diagonal', 'diff', 'digitize', 'divide', 'dot',
+ 'double', 'dsplit', 'dstack', 'dtype', 'e', 'ediff1d',
+ 'empty', 'empty_like', 'equal', 'exp', 'exp2', 'expand_dims',
+ 'expm1', 'extract', 'eye', 'fabs', 'fill_diagonal', 'finfo',
+ 'fix', 'flatiter', 'flatnonzero', 'fliplr', 'flipud',
+ 'float', 'float32', 'float64', 'float_', 'floating', 'floor',
+ 'floor_divide', 'fmax', 'fmin', 'fmod', 'format_parser',
+ 'frexp', 'frombuffer', 'fromfile', 'fromfunction',
+ 'fromiter', 'frompyfunc', 'fromregex', 'fromstring', 'fv',
+ 'genfromtxt', 'getbufsize', 'geterr', 'gradient', 'greater',
+ 'greater_equal', 'hamming', 'hanning', 'histogram',
+ 'histogram2d', 'histogramdd', 'hsplit', 'hstack', 'hypot',
+ 'i0', 'identity', 'iinfo', 'imag', 'in1d', 'index_exp',
+ 'indices', 'inexact', 'inf', 'info', 'infty', 'inner',
+ 'insert', 'int', 'int0', 'int16', 'int32', 'int64', 'int8',
+ 'int_', 'int_asbuffer', 'intc', 'integer', 'interp',
+ 'intersect1d', 'intp', 'invert', 'ipmt', 'irr', 'iscomplex',
+ 'iscomplexobj', 'isfinite', 'isfortran', 'isinf', 'isnan',
+ 'isneginf', 'isposinf', 'isreal', 'isrealobj', 'isscalar',
+ 'issctype', 'iterable', 'ix_', 'kaiser', 'kron', 'ldexp',
+ 'left_shift', 'less', 'less_equal', 'linspace',
+ 'little_endian', 'load', 'loads', 'loadtxt', 'log', 'log10',
+ 'log1p', 'log2', 'logaddexp', 'logaddexp2', 'logical_and',
+ 'logical_not', 'logical_or', 'logical_xor', 'logspace',
+ 'long', 'longcomplex', 'longdouble', 'longfloat', 'longlong',
+ 'mafromtxt', 'mask_indices', 'mat', 'matrix', 'max',
+ 'maximum', 'maximum_sctype', 'may_share_memory', 'mean',
+ 'median', 'memmap', 'meshgrid', 'mgrid', 'min', 'minimum',
+ 'mintypecode', 'mirr', 'mod', 'modf', 'msort', 'multiply',
+ 'nan', 'nan_to_num', 'nanargmax', 'nanargmin', 'nanmax',
+ 'nanmin', 'nansum', 'ndarray', 'ndenumerate', 'ndfromtxt',
+ 'ndim', 'ndindex', 'negative', 'newaxis', 'nextafter',
+ 'nonzero', 'not_equal', 'nper', 'npv', 'number',
+ 'obj2sctype', 'ogrid', 'ones', 'ones_like', 'outer',
+ 'packbits', 'percentile', 'pi', 'piecewise', 'place', 'pmt',
+ 'poly', 'poly1d', 'polyadd', 'polyder', 'polydiv', 'polyfit',
+ 'polyint', 'polymul', 'polysub', 'polyval', 'power', 'ppmt',
+ 'prod', 'product', 'ptp', 'put', 'putmask', 'pv', 'r_',
+ 'rad2deg', 'radians', 'rank', 'rate', 'ravel', 'real',
+ 'real_if_close', 'reciprocal', 'record', 'remainder',
+ 'repeat', 'reshape', 'resize', 'restoredot', 'right_shift',
+ 'rint', 'roll', 'rollaxis', 'roots', 'rot90', 'round',
+ 'round_', 'row_stack', 's_', 'sctype2char', 'searchsorted',
+ 'select', 'setbufsize', 'setdiff1d', 'seterr', 'setxor1d',
+ 'shape', 'short', 'sign', 'signbit', 'signedinteger', 'sin',
+ 'sinc', 'single', 'singlecomplex', 'sinh', 'size',
+ 'sometrue', 'sort', 'sort_complex', 'spacing', 'split',
+ 'sqrt', 'square', 'squeeze', 'std', 'str', 'str_',
+ 'subtract', 'sum', 'swapaxes', 'take', 'tan', 'tanh',
+ 'tensordot', 'tile', 'trace', 'transpose', 'trapz', 'tri',
+ 'tril', 'tril_indices', 'tril_indices_from', 'trim_zeros',
+ 'triu', 'triu_indices', 'triu_indices_from', 'true_divide',
+ 'trunc', 'ubyte', 'uint', 'uint0', 'uint16', 'uint32',
+ 'uint64', 'uint8', 'uintc', 'uintp', 'ulonglong', 'union1d',
+ 'unique', 'unravel_index', 'unsignedinteger', 'unwrap',
+ 'ushort', 'vander', 'var', 'vdot', 'vectorize', 'vsplit',
+ 'vstack', 'where', 'who', 'zeros', 'zeros_like')
+
+NUMPY_RENAMES = {'ln': 'log', 'asin': 'arcsin', 'acos': 'arccos',
+ 'atan': 'arctan', 'atan2': 'arctan2', 'atanh':
+ 'arctanh', 'acosh': 'arccosh', 'asinh': 'arcsinh'}
+
+def _open(filename, mode='r', buffering=0):
+ """read only version of open()"""
+ umode = 'r'
+ if mode == 'rb':
+ umode = 'rb'
+ return open(filename, umode, buffering)
+
+LOCALFUNCS = {'open': _open}
+
+OPERATORS = {ast.Is: lambda a, b: a is b,
+ ast.IsNot: lambda a, b: a is not b,
+ ast.In: lambda a, b: a in b,
+ ast.NotIn: lambda a, b: a not in b,
+ ast.Add: lambda a, b: a + b,
+ ast.BitAnd: lambda a, b: a & b,
+ ast.BitOr: lambda a, b: a | b,
+ ast.BitXor: lambda a, b: a ^ b,
+ ast.Div: lambda a, b: a / b,
+ ast.FloorDiv: lambda a, b: a // b,
+ ast.LShift: lambda a, b: a << b,
+ ast.RShift: lambda a, b: a >> b,
+ ast.Mult: lambda a, b: a * b,
+ ast.Pow: lambda a, b: a ** b,
+ ast.Sub: lambda a, b: a - b,
+ ast.Mod: lambda a, b: a % b,
+ ast.And: lambda a, b: a and b,
+ ast.Or: lambda a, b: a or b,
+ ast.Eq: lambda a, b: a == b,
+ ast.Gt: lambda a, b: a > b,
+ ast.GtE: lambda a, b: a >= b,
+ ast.Lt: lambda a, b: a < b,
+ ast.LtE: lambda a, b: a <= b,
+ ast.NotEq: lambda a, b: a != b,
+ ast.Invert: lambda a: ~a,
+ ast.Not: lambda a: not a,
+ ast.UAdd: lambda a: +a,
+ ast.USub: lambda a: -a}
+
+
+def valid_symbol_name(name):
+ """determines whether the input symbol name is a valid name
+
+ This checks for reserved words, and that the name matches the
+ regular expression ``[a-zA-Z_][a-zA-Z0-9_]``
+ """
+ if name in RESERVED_WORDS:
+ return False
+ return NAME_MATCH(name) is not None
+
+
+def op2func(op):
+ "return function for operator nodes"
+ return OPERATORS[op.__class__]
+
+
+class Empty:
+ """empty class"""
+ def __init__(self):
+ pass
+
+ def __nonzero__(self):
+ return False
+
+ReturnedNone = Empty()
+
+
+class ExceptionHolder(object):
+ "basic exception handler"
+ def __init__(self, node, exc=None, msg='', expr=None, lineno=None):
+ self.node = node
+ self.expr = expr
+ self.msg = msg
+ self.exc = exc
+ self.lineno = lineno
+ self.exc_info = exc_info()
+ if self.exc is None and self.exc_info[0] is not None:
+ self.exc = self.exc_info[0]
+ if self.msg is '' and self.exc_info[1] is not None:
+ self.msg = self.exc_info[1]
+
+ def get_error(self):
+ "retrieve error data"
+ col_offset = -1
+ if self.node is not None:
+ try:
+ col_offset = self.node.col_offset
+ except AttributeError:
+ pass
+ try:
+ exc_name = self.exc.__name__
+ except AttributeError:
+ exc_name = str(self.exc)
+ if exc_name in (None, 'None'):
+ exc_name = 'UnknownError'
+
+ out = [" %s" % self.expr]
+ if col_offset > 0:
+ out.append(" %s^^^" % ((col_offset)*' '))
+ out.append(str(self.msg))
+ return (exc_name, '\n'.join(out))
+
+
+class NameFinder(ast.NodeVisitor):
+ """find all symbol names used by a parsed node"""
+ def __init__(self):
+ self.names = []
+ ast.NodeVisitor.__init__(self)
+
+ def generic_visit(self, node):
+ if node.__class__.__name__ == 'Name':
+ if node.ctx.__class__ == ast.Load and node.id not in self.names:
+ self.names.append(node.id)
+ ast.NodeVisitor.generic_visit(self, node)
+
+def get_ast_names(astnode):
+ "returns symbol Names from an AST node"
+ finder = NameFinder()
+ finder.generic_visit(astnode)
+ return finder.names
diff --git a/lmfit/confidence.py b/lmfit/confidence.py
index d8a2934..b1bce11 100644
--- a/lmfit/confidence.py
+++ b/lmfit/confidence.py
@@ -1,419 +1,416 @@
-#!/usr/bin/python
-# -*- coding: utf-8 -*-
-"""
-Contains functions to calculate confidence intervals.
-"""
-from __future__ import print_function
-from warnings import warn
-import numpy as np
-from scipy.stats import f
-from scipy.optimize import brentq
-from .minimizer import MinimizerException
-
-try:
- from collections import OrderedDict
-except ImportError:
- from ordereddict import OrderedDict
-
-CONF_ERR_GEN = 'Cannot determine Confidence Intervals'
-CONF_ERR_STDERR = '%s without sensible uncertainty estimates' % CONF_ERR_GEN
-CONF_ERR_NVARS = '%s with < 2 variables' % CONF_ERR_GEN
-
-def f_compare(ndata, nparas, new_chi, best_chi, nfix=1.):
- """
- Returns the probalitiy for two given parameter sets.
- nfix is the number of fixed parameters.
- """
- nparas = nparas + nfix
- nfree = ndata - nparas
- nfix = 1.0*nfix
- dchi = new_chi / best_chi - 1.0
- return f.cdf(dchi * nfree / nfix, nfix, nfree)
-
-
-def copy_vals(params):
- """Saves the values and stderrs of params in temporay dict"""
- tmp_params = {}
- for para_key in params:
- tmp_params[para_key] = (params[para_key].value,
- params[para_key].stderr)
- return tmp_params
-
-
-def restore_vals(tmp_params, params):
- """Restores values and stderrs of params in temporay dict"""
- for para_key in params:
- params[para_key].value, params[para_key].stderr = tmp_params[para_key]
-
-
-def conf_interval(minimizer, result, p_names=None, sigmas=(0.674, 0.95, 0.997),
- trace=False, maxiter=200, verbose=False, prob_func=None):
- r"""Calculates the confidence interval for parameters
- from the given a MinimizerResult, output from minimize.
-
- The parameter for which the ci is calculated will be varied, while
- the remaining parameters are re-optimized for minimizing chi-square.
- The resulting chi-square is used to calculate the probability with
- a given statistic e.g. F-statistic. This function uses a 1d-rootfinder
- from scipy to find the values resulting in the searched confidence
- region.
-
- Parameters
- ----------
- minimizer : Minimizer
- The minimizer to use, holding objective function.
- result : MinimizerResult
- The result of running minimize().
- p_names : list, optional
- Names of the parameters for which the ci is calculated. If None,
- the ci is calculated for every parameter.
- sigmas : list, optional
- The probabilities (1-alpha) to find. Default is 1,2 and 3-sigma.
- trace : bool, optional
- Defaults to False, if true, each result of a probability calculation
- is saved along with the parameter. This can be used to plot so
- called "profile traces".
-
- Returns
- -------
- output : dict
- A dict, which contains a list of (sigma, vals)-tuples for each name.
- trace_dict : dict
- Only if trace is set true. Is a dict, the key is the parameter which
- was fixed.The values are again a dict with the names as keys, but with
- an additional key 'prob'. Each contains an array of the corresponding
- values.
-
- See also
- --------
- conf_interval2d
-
- Other Parameters
- ----------------
- maxiter : int
- Maximum of iteration to find an upper limit.
- prob_func : ``None`` or callable
- Function to calculate the probability from the optimized chi-square.
- Default (``None``) uses built-in f_compare (F test).
- verbose: bool
- print extra debuggin information. Default is ``False``.
-
-
- Examples
- --------
-
- >>> from lmfit.printfuncs import *
- >>> mini = minimize(some_func, params)
- >>> mini.leastsq()
- True
- >>> report_errors(params)
- ... #report
- >>> ci = conf_interval(mini)
- >>> report_ci(ci)
- ... #report
-
- Now with quantiles for the sigmas and using the trace.
-
- >>> ci, trace = conf_interval(mini, sigmas=(0.25, 0.5, 0.75, 0.999), trace=True)
- >>> fixed = trace['para1']['para1']
- >>> free = trace['para1']['not_para1']
- >>> prob = trace['para1']['prob']
-
- This makes it possible to plot the dependence between free and fixed.
- """
- ci = ConfidenceInterval(minimizer, result, p_names, prob_func, sigmas,
- trace, verbose, maxiter)
- output = ci.calc_all_ci()
- if trace:
- return output, ci.trace_dict
- return output
-
-
-def map_trace_to_names(trace, params):
- "maps trace to param names"
- out = {}
- allnames = list(params.keys()) + ['prob']
- for name in trace.keys():
- tmp_dict = {}
- tmp = np.array(trace[name])
- for para_name, values in zip(allnames, tmp.T):
- tmp_dict[para_name] = values
- out[name] = tmp_dict
- return out
-
-
-class ConfidenceInterval(object):
- """
- Class used to calculate the confidence interval.
- """
- def __init__(self, minimizer, result, p_names=None, prob_func=None,
- sigmas=(0.674, 0.95, 0.997), trace=False, verbose=False,
- maxiter=50):
- """
-
- """
- self.verbose = verbose
- self.minimizer = minimizer
- self.result = result
- self.params = result.params
- self.org = copy_vals(self.params)
- self.best_chi = result.chisqr
-
- if p_names is None:
- p_names = [i for i in self.params if self.params[i].vary]
-
- self.p_names = p_names
- self.fit_params = [self.params[p] for p in self.p_names]
-
- # check that there are at least 2 true variables!
- # check that all stderrs are sensible (including not None or NaN)
- nvars = 0
- for par in self.fit_params:
- if par.vary:
- nvars += 1
- try:
- if not (par.vary and par.stderr > 0.0):
- raise MinimizerException(CONF_ERR_STDERR)
- except TypeError:
- raise MinimizerException(CONF_ERR_STDERR)
- if nvars < 2:
- raise MinimizerException(CONF_ERR_NVARS)
-
- if prob_func is None or not hasattr(prob_func, '__call__'):
- self.prob_func = f_compare
- if trace:
- self.trace_dict = dict([(i, []) for i in self.p_names])
-
- self.trace = trace
- self.maxiter = maxiter
- self.min_rel_change = 1e-5
-
- self.sigmas = list(sigmas)
- self.sigmas.sort()
-
- def calc_all_ci(self):
- """
- Calculates all cis.
- """
- out = OrderedDict()
-
- for p in self.p_names:
- out[p] = (self.calc_ci(p, -1)[::-1] +
- [(0., self.params[p].value)] +
- self.calc_ci(p, 1))
- if self.trace:
- self.trace_dict = map_trace_to_names(self.trace_dict,
- self.params)
-
- return out
-
- def calc_ci(self, para, direction):
- """
- Calculate the ci for a single parameter for a single direction.
- Direction is either positive or negative 1.
- """
-
- if isinstance(para, str):
- para = self.params[para]
-
- #function used to calculate the pro
- calc_prob = lambda val, prob: self.calc_prob(para, val, prob)
- if self.trace:
- x = [i.value for i in self.params.values()]
- self.trace_dict[para.name].append(x + [0])
-
- para.vary = False
- limit, max_prob = self.find_limit(para, direction)
- start_val = para.value.copy()
- a_limit = start_val.copy()
- ret = []
- orig_warn_settings = np.geterr()
- np.seterr(all='ignore')
- for prob in self.sigmas:
- if prob > max_prob:
- ret.append((prob, direction*np.inf))
- continue
-
- try:
- val = brentq(calc_prob, a_limit,
- limit, rtol=.5e-4, args=prob)
-
- except ValueError:
- self.reset_vals()
- try:
- val = brentq(calc_prob, start_val,
- limit, rtol=.5e-4, args=prob)
- except ValueError:
- val = np.nan
-
- a_limit = val
- ret.append((prob, val))
-
- para.vary = True
- self.reset_vals()
- np.seterr(**orig_warn_settings)
- return ret
-
- def reset_vals(self):
- restore_vals(self.org, self.params)
-
- def find_limit(self, para, direction):
- """
- For given para, search a value so that prob(val) > sigmas.
- """
- if self.verbose:
- print('Calculating CI for ' + para.name)
- self.reset_vals()
-
- #starting steps:
- if para.stderr > 0 and para.stderr < abs(para.value):
- step = para.stderr
- else:
- step = max(abs(para.value) * 0.2, 0.001)
- para.vary = False
- start_val = para.value
-
- old_prob = 0
- limit = start_val
- i = 0
-
- while old_prob < max(self.sigmas):
- i = i + 1
- limit += step * direction
-
- new_prob = self.calc_prob(para, limit)
- rel_change = (new_prob - old_prob) / max(new_prob, old_prob, 1.e-12)
- old_prob = new_prob
-
- # Check convergence.
- if i > self.maxiter:
- errmsg = "Warning, maxiter={0} reached".format(self.maxiter)
- errmsg += "and prob({0}={1}) = {2} < max(sigmas).".format(para.name, limit, new_prob)
- warn(errmsg)
- break
-
- if rel_change < self.min_rel_change:
- errmsg = "Warning, rel_change={0} < 0.01 ".format(rel_change)
- errmsg += " at iteration {3} and prob({0}={1}) = {2} < max(sigmas).".format(para.name, limit, new_prob, i)
- warn(errmsg)
- break
-
- self.reset_vals()
-
- return limit, new_prob
-
- def calc_prob(self, para, val, offset=0., restore=False):
- """Returns the probability for given Value."""
- if restore:
- restore_vals(self.org, self.params)
- para.value = val
- save_para = self.params[para.name]
- self.params[para.name] = para
- self.minimizer.prepare_fit(self.params)
- out = self.minimizer.leastsq()
- prob = self.prob_func(out.ndata, out.ndata - out.nfree,
- out.chisqr, self.best_chi)
-
- if self.trace:
- x = [i.value for i in out.params.values()]
- self.trace_dict[para.name].append(x + [prob])
- self.params[para.name] = save_para
- return prob - offset
-
-def conf_interval2d(minimizer, result, x_name, y_name, nx=10, ny=10,
- limits=None, prob_func=None):
- r"""Calculates confidence regions for two fixed parameters.
-
- The method is explained in *conf_interval*: here we are fixing
- two parameters.
-
- Parameters
- ----------
- minimizer : Minimizer
- The minimizer to use, holding objective function.
- result : MinimizerResult
- The result of running minimize().
- x_name : string
- The name of the parameter which will be the x direction.
- y_name : string
- The name of the parameter which will be the y direction.
- nx, ny : ints, optional
- Number of points.
- limits : tuple: optional
- Should have the form ((x_upper, x_lower),(y_upper, y_lower)). If not
- given, the default is 5 std-errs in each direction.
-
- Returns
- -------
- x : (nx)-array
- x-coordinates
- y : (ny)-array
- y-coordinates
- grid : (nx,ny)-array
- grid contains the calculated probabilities.
-
- Examples
- --------
-
- >>> mini = Minimizer(some_func, params)
- >>> result = mini.leastsq()
- >>> x, y, gr = conf_interval2d(mini, result, 'para1','para2')
- >>> plt.contour(x,y,gr)
-
- Other Parameters
- ----------------
- prob_func : ``None`` or callable
- Function to calculate the probability from the optimized chi-square.
- Default (``None``) uses built-in f_compare (F test).
- """
- # used to detect that .leastsq() has run!
- params = result.params
-
- best_chi = result.chisqr
- org = copy_vals(result.params)
-
- if prob_func is None or not hasattr(prob_func, '__call__'):
- prob_func = f_compare
-
- x = params[x_name]
- y = params[y_name]
-
- if limits is None:
- (x_upper, x_lower) = (x.value + 5 * x.stderr, x.value - 5
- * x.stderr)
- (y_upper, y_lower) = (y.value + 5 * y.stderr, y.value - 5
- * y.stderr)
- elif len(limits) == 2:
- (x_upper, x_lower) = limits[0]
- (y_upper, y_lower) = limits[1]
-
- x_points = np.linspace(x_lower, x_upper, nx)
- y_points = np.linspace(y_lower, y_upper, ny)
- grid = np.dstack(np.meshgrid(x_points, y_points))
-
- x.vary = False
- y.vary = False
-
- def calc_prob(vals, restore=False):
- if restore:
- restore_vals(org, result.params)
- x.value = vals[0]
- y.value = vals[1]
- save_x = result.params[x.name]
- save_y = result.params[y.name]
- result.params[x.name] = x
- result.params[y.name] = y
- minimizer.prepare_fit(params=result.params)
- out = minimizer.leastsq()
- prob = prob_func(out.ndata, out.ndata - out.nfree, out.chisqr,
- best_chi, nfix=2.)
- result.params[x.name] = save_x
- result.params[y.name] = save_y
- return prob
-
- out = x_points, y_points, np.apply_along_axis(calc_prob, -1, grid)
-
- x.vary, y.vary = True, True
- restore_vals(org, result.params)
- result.chisqr = best_chi
- return out
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+"""
+Contains functions to calculate confidence intervals.
+"""
+from __future__ import print_function
+from warnings import warn
+import numpy as np
+from scipy.stats import f
+from scipy.optimize import brentq
+from .minimizer import MinimizerException
+
+try:
+ from collections import OrderedDict
+except ImportError:
+ from ordereddict import OrderedDict
+
+CONF_ERR_GEN = 'Cannot determine Confidence Intervals'
+CONF_ERR_STDERR = '%s without sensible uncertainty estimates' % CONF_ERR_GEN
+CONF_ERR_NVARS = '%s with < 2 variables' % CONF_ERR_GEN
+
+def f_compare(ndata, nparas, new_chi, best_chi, nfix=1.):
+ """
+ Returns the probalitiy for two given parameter sets.
+ nfix is the number of fixed parameters.
+ """
+ nparas = nparas + nfix
+ nfree = ndata - nparas
+ nfix = 1.0*nfix
+ dchi = new_chi / best_chi - 1.0
+ return f.cdf(dchi * nfree / nfix, nfix, nfree)
+
+
+def copy_vals(params):
+ """Saves the values and stderrs of params in temporay dict"""
+ tmp_params = {}
+ for para_key in params:
+ tmp_params[para_key] = (params[para_key].value,
+ params[para_key].stderr)
+ return tmp_params
+
+
+def restore_vals(tmp_params, params):
+ """Restores values and stderrs of params in temporay dict"""
+ for para_key in params:
+ params[para_key].value, params[para_key].stderr = tmp_params[para_key]
+
+
+def conf_interval(minimizer, result, p_names=None, sigmas=(0.674, 0.95, 0.997),
+ trace=False, maxiter=200, verbose=False, prob_func=None):
+ """Calculates the confidence interval for parameters
+ from the given a MinimizerResult, output from minimize.
+
+ The parameter for which the ci is calculated will be varied, while
+ the remaining parameters are re-optimized for minimizing chi-square.
+ The resulting chi-square is used to calculate the probability with
+ a given statistic e.g. F-statistic. This function uses a 1d-rootfinder
+ from scipy to find the values resulting in the searched confidence
+ region.
+
+ Parameters
+ ----------
+ minimizer : Minimizer
+ The minimizer to use, holding objective function.
+ result : MinimizerResult
+ The result of running minimize().
+ p_names : list, optional
+ Names of the parameters for which the ci is calculated. If None,
+ the ci is calculated for every parameter.
+ sigmas : list, optional
+ The probabilities (1-alpha) to find. Default is 1,2 and 3-sigma.
+ trace : bool, optional
+ Defaults to False, if true, each result of a probability calculation
+ is saved along with the parameter. This can be used to plot so
+ called "profile traces".
+ maxiter : int
+ Maximum of iteration to find an upper limit. Default is 200.
+ prob_func : ``None`` or callable
+ Function to calculate the probability from the optimized chi-square.
+ Default (``None``) uses built-in f_compare (F test).
+ verbose: bool
+ print extra debuging information. Default is ``False``.
+
+
+ Returns
+ -------
+ output : dict
+ A dict, which contains a list of (sigma, vals)-tuples for each name.
+ trace_dict : dict
+ Only if trace is set true. Is a dict, the key is the parameter which
+ was fixed. The values are again a dict with the names as keys, but with
+ an additional key 'prob'. Each contains an array of the corresponding
+ values.
+
+ See also
+ --------
+ conf_interval2d
+
+ Examples
+ --------
+
+ >>> from lmfit.printfuncs import *
+ >>> mini = minimize(some_func, params)
+ >>> mini.leastsq()
+ True
+ >>> report_errors(params)
+ ... #report
+ >>> ci = conf_interval(mini)
+ >>> report_ci(ci)
+ ... #report
+
+ Now with quantiles for the sigmas and using the trace.
+
+ >>> ci, trace = conf_interval(mini, sigmas=(0.25, 0.5, 0.75, 0.999), trace=True)
+ >>> fixed = trace['para1']['para1']
+ >>> free = trace['para1']['not_para1']
+ >>> prob = trace['para1']['prob']
+
+ This makes it possible to plot the dependence between free and fixed.
+
+ """
+ ci = ConfidenceInterval(minimizer, result, p_names, prob_func, sigmas,
+ trace, verbose, maxiter)
+ output = ci.calc_all_ci()
+ if trace:
+ return output, ci.trace_dict
+ return output
+
+
+def map_trace_to_names(trace, params):
+ "maps trace to param names"
+ out = {}
+ allnames = list(params.keys()) + ['prob']
+ for name in trace.keys():
+ tmp_dict = {}
+ tmp = np.array(trace[name])
+ for para_name, values in zip(allnames, tmp.T):
+ tmp_dict[para_name] = values
+ out[name] = tmp_dict
+ return out
+
+
+class ConfidenceInterval(object):
+ """
+ Class used to calculate the confidence interval.
+ """
+ def __init__(self, minimizer, result, p_names=None, prob_func=None,
+ sigmas=(0.674, 0.95, 0.997), trace=False, verbose=False,
+ maxiter=50):
+ """
+
+ """
+ self.verbose = verbose
+ self.minimizer = minimizer
+ self.result = result
+ self.params = result.params
+ self.org = copy_vals(self.params)
+ self.best_chi = result.chisqr
+
+ if p_names is None:
+ p_names = [i for i in self.params if self.params[i].vary]
+
+ self.p_names = p_names
+ self.fit_params = [self.params[p] for p in self.p_names]
+
+ # check that there are at least 2 true variables!
+ # check that all stderrs are sensible (including not None or NaN)
+ nvars = 0
+ for par in self.fit_params:
+ if par.vary:
+ nvars += 1
+ try:
+ if not (par.vary and par.stderr > 0.0):
+ raise MinimizerException(CONF_ERR_STDERR)
+ except TypeError:
+ raise MinimizerException(CONF_ERR_STDERR)
+ if nvars < 2:
+ raise MinimizerException(CONF_ERR_NVARS)
+
+ if prob_func is None or not hasattr(prob_func, '__call__'):
+ self.prob_func = f_compare
+ if trace:
+ self.trace_dict = dict([(i, []) for i in self.p_names])
+
+ self.trace = trace
+ self.maxiter = maxiter
+ self.min_rel_change = 1e-5
+
+ self.sigmas = list(sigmas)
+ self.sigmas.sort()
+
+ def calc_all_ci(self):
+ """
+ Calculates all cis.
+ """
+ out = OrderedDict()
+
+ for p in self.p_names:
+ out[p] = (self.calc_ci(p, -1)[::-1] +
+ [(0., self.params[p].value)] +
+ self.calc_ci(p, 1))
+ if self.trace:
+ self.trace_dict = map_trace_to_names(self.trace_dict,
+ self.params)
+
+ return out
+
+ def calc_ci(self, para, direction):
+ """
+ Calculate the ci for a single parameter for a single direction.
+ Direction is either positive or negative 1.
+ """
+
+ if isinstance(para, str):
+ para = self.params[para]
+
+ #function used to calculate the pro
+ calc_prob = lambda val, prob: self.calc_prob(para, val, prob)
+ if self.trace:
+ x = [i.value for i in self.params.values()]
+ self.trace_dict[para.name].append(x + [0])
+
+ para.vary = False
+ limit, max_prob = self.find_limit(para, direction)
+ start_val = a_limit = float(para.value)
+ ret = []
+ orig_warn_settings = np.geterr()
+ np.seterr(all='ignore')
+ for prob in self.sigmas:
+ if prob > max_prob:
+ ret.append((prob, direction*np.inf))
+ continue
+
+ try:
+ val = brentq(calc_prob, a_limit,
+ limit, rtol=.5e-4, args=prob)
+
+ except ValueError:
+ self.reset_vals()
+ try:
+ val = brentq(calc_prob, start_val,
+ limit, rtol=.5e-4, args=prob)
+ except ValueError:
+ val = np.nan
+
+ a_limit = val
+ ret.append((prob, val))
+
+ para.vary = True
+ self.reset_vals()
+ np.seterr(**orig_warn_settings)
+ return ret
+
+ def reset_vals(self):
+ restore_vals(self.org, self.params)
+
+ def find_limit(self, para, direction):
+ """
+ For given para, search a value so that prob(val) > sigmas.
+ """
+ if self.verbose:
+ print('Calculating CI for ' + para.name)
+ self.reset_vals()
+
+ #starting steps:
+ if para.stderr > 0 and para.stderr < abs(para.value):
+ step = para.stderr
+ else:
+ step = max(abs(para.value) * 0.2, 0.001)
+ para.vary = False
+ start_val = para.value
+
+ old_prob = 0
+ limit = start_val
+ i = 0
+
+ while old_prob < max(self.sigmas):
+ i = i + 1
+ limit += step * direction
+
+ new_prob = self.calc_prob(para, limit)
+ rel_change = (new_prob - old_prob) / max(new_prob, old_prob, 1.e-12)
+ old_prob = new_prob
+
+ # Check convergence.
+ if i > self.maxiter:
+ errmsg = "Warning, maxiter={0} reached".format(self.maxiter)
+ errmsg += "and prob({0}={1}) = {2} < max(sigmas).".format(para.name, limit, new_prob)
+ warn(errmsg)
+ break
+
+ if rel_change < self.min_rel_change:
+ errmsg = "Warning, rel_change={0} < 0.01 ".format(rel_change)
+ errmsg += " at iteration {3} and prob({0}={1}) = {2} < max(sigmas).".format(para.name, limit, new_prob, i)
+ warn(errmsg)
+ break
+
+ self.reset_vals()
+
+ return limit, new_prob
+
+ def calc_prob(self, para, val, offset=0., restore=False):
+ """Returns the probability for given Value."""
+ if restore:
+ restore_vals(self.org, self.params)
+ para.value = val
+ save_para = self.params[para.name]
+ self.params[para.name] = para
+ self.minimizer.prepare_fit(self.params)
+ out = self.minimizer.leastsq()
+ prob = self.prob_func(out.ndata, out.ndata - out.nfree,
+ out.chisqr, self.best_chi)
+
+ if self.trace:
+ x = [i.value for i in out.params.values()]
+ self.trace_dict[para.name].append(x + [prob])
+ self.params[para.name] = save_para
+ return prob - offset
+
+def conf_interval2d(minimizer, result, x_name, y_name, nx=10, ny=10,
+ limits=None, prob_func=None):
+ r"""Calculates confidence regions for two fixed parameters.
+
+ The method is explained in *conf_interval*: here we are fixing
+ two parameters.
+
+ Parameters
+ ----------
+ minimizer : Minimizer
+ The minimizer to use, holding objective function.
+ result : MinimizerResult
+ The result of running minimize().
+ x_name : string
+ The name of the parameter which will be the x direction.
+ y_name : string
+ The name of the parameter which will be the y direction.
+ nx, ny : ints, optional
+ Number of points.
+ limits : tuple: optional
+ Should have the form ((x_upper, x_lower),(y_upper, y_lower)). If not
+ given, the default is 5 std-errs in each direction.
+
+ Returns
+ -------
+ x : (nx)-array
+ x-coordinates
+ y : (ny)-array
+ y-coordinates
+ grid : (nx,ny)-array
+ grid contains the calculated probabilities.
+
+ Examples
+ --------
+
+ >>> mini = Minimizer(some_func, params)
+ >>> result = mini.leastsq()
+ >>> x, y, gr = conf_interval2d(mini, result, 'para1','para2')
+ >>> plt.contour(x,y,gr)
+
+ Other Parameters
+ ----------------
+ prob_func : ``None`` or callable
+ Function to calculate the probability from the optimized chi-square.
+ Default (``None``) uses built-in f_compare (F test).
+ """
+ # used to detect that .leastsq() has run!
+ params = result.params
+
+ best_chi = result.chisqr
+ org = copy_vals(result.params)
+
+ if prob_func is None or not hasattr(prob_func, '__call__'):
+ prob_func = f_compare
+
+ x = params[x_name]
+ y = params[y_name]
+
+ if limits is None:
+ (x_upper, x_lower) = (x.value + 5 * x.stderr, x.value - 5
+ * x.stderr)
+ (y_upper, y_lower) = (y.value + 5 * y.stderr, y.value - 5
+ * y.stderr)
+ elif len(limits) == 2:
+ (x_upper, x_lower) = limits[0]
+ (y_upper, y_lower) = limits[1]
+
+ x_points = np.linspace(x_lower, x_upper, nx)
+ y_points = np.linspace(y_lower, y_upper, ny)
+ grid = np.dstack(np.meshgrid(x_points, y_points))
+
+ x.vary = False
+ y.vary = False
+
+ def calc_prob(vals, restore=False):
+ if restore:
+ restore_vals(org, result.params)
+ x.value = vals[0]
+ y.value = vals[1]
+ save_x = result.params[x.name]
+ save_y = result.params[y.name]
+ result.params[x.name] = x
+ result.params[y.name] = y
+ minimizer.prepare_fit(params=result.params)
+ out = minimizer.leastsq()
+ prob = prob_func(out.ndata, out.ndata - out.nfree, out.chisqr,
+ best_chi, nfix=2.)
+ result.params[x.name] = save_x
+ result.params[y.name] = save_y
+ return prob
+
+ out = x_points, y_points, np.apply_along_axis(calc_prob, -1, grid)
+
+ x.vary, y.vary = True, True
+ restore_vals(org, result.params)
+ result.chisqr = best_chi
+ return out
diff --git a/lmfit/lineshapes.py b/lmfit/lineshapes.py
index a71bb3f..6c55279 100644
--- a/lmfit/lineshapes.py
+++ b/lmfit/lineshapes.py
@@ -1,286 +1,286 @@
-#!/usr/bin/env python
-"""
-basic model line shapes and distribution functions
-"""
-from __future__ import division
-from numpy import (pi, log, exp, sqrt, arctan, cos, where)
-from numpy.testing import assert_allclose
-
-from scipy.special import gamma as gamfcn
-from scipy.special import gammaln, erf, erfc, wofz
-
-log2 = log(2)
-s2pi = sqrt(2*pi)
-spi = sqrt(pi)
-s2 = sqrt(2.0)
-
-functions = ('gaussian', 'lorentzian', 'voigt', 'pvoigt', 'moffat', 'pearson7',
- 'breit_wigner', 'damped_oscillator', 'logistic', 'lognormal',
- 'students_t', 'expgaussian', 'donaich', 'skewed_gaussian',
- 'skewed_voigt', 'step', 'rectangle', 'erf', 'erfc', 'wofz',
- 'gamma', 'gammaln', 'exponential', 'powerlaw', 'linear',
- 'parabolic')
-
-def gaussian(x, amplitude=1.0, center=0.0, sigma=1.0):
- """1 dimensional gaussian:
- gaussian(x, amplitude, center, sigma)
- """
- return (amplitude/(s2pi*sigma)) * exp(-(1.0*x-center)**2 /(2*sigma**2))
-
-def lorentzian(x, amplitude=1.0, center=0.0, sigma=1.0):
- """1 dimensional lorentzian
- lorentzian(x, amplitude, center, sigma)
- """
- return (amplitude/(1 + ((1.0*x-center)/sigma)**2) ) / (pi*sigma)
-
-def voigt(x, amplitude=1.0, center=0.0, sigma=1.0, gamma=None):
- """1 dimensional voigt function.
- see http://en.wikipedia.org/wiki/Voigt_profile
- """
- if gamma is None:
- gamma = sigma
- z = (x-center + 1j*gamma)/ (sigma*s2)
- return amplitude*wofz(z).real / (sigma*s2pi)
-
-def pvoigt(x, amplitude=1.0, center=0.0, sigma=1.0, fraction=0.5):
- """1 dimensional pseudo-voigt:
- pvoigt(x, amplitude, center, sigma, fraction)
- = amplitude*(1-fraction)*gaussion(x, center, sigma_g) +
- amplitude*fraction*lorentzian(x, center, sigma)
-
- where sigma_g (the sigma for the Gaussian component) is
-
- sigma_g = sigma / sqrt(2*log(2)) ~= sigma / 1.17741
-
- so that the Gaussian and Lorentzian components have the
- same FWHM of 2*sigma.
- """
- sigma_g = sigma / sqrt(2*log2)
- return ((1-fraction)*gaussian(x, amplitude, center, sigma_g) +
- fraction*lorentzian(x, amplitude, center, sigma))
-
-def moffat(x, amplitude=1, center=0., sigma=1, beta=1.):
- """ 1 dimensional moffat function:
-
- moffat(amplitude, center, sigma, beta) = amplitude / (((x - center)/sigma)**2 + 1)**beta
- """
- return amplitude / (((x - center)/sigma)**2 + 1)**beta
-
-def pearson7(x, amplitude=1.0, center=0.0, sigma=1.0, expon=1.0):
- """pearson7 lineshape, using the wikipedia definition:
-
- pearson7(x, center, sigma, expon) =
- amplitude*(1+arg**2)**(-expon)/(sigma*beta(expon-0.5, 0.5))
-
- where arg = (x-center)/sigma
- and beta() is the beta function.
- """
- arg = (x-center)/sigma
- scale = amplitude * gamfcn(expon)/(gamfcn(0.5)*gamfcn(expon-0.5))
- return scale*(1+arg**2)**(-expon)/sigma
-
-def breit_wigner(x, amplitude=1.0, center=0.0, sigma=1.0, q=1.0):
- """Breit-Wigner-Fano lineshape:
- = amplitude*(q*sigma/2 + x - center)**2 / ( (sigma/2)**2 + (x - center)**2 )
- """
- gam = sigma/2.0
- return amplitude*(q*gam + x - center)**2 / (gam*gam + (x-center)**2)
-
-def damped_oscillator(x, amplitude=1.0, center=1., sigma=0.1):
- """amplitude for a damped harmonic oscillator
- amplitude/sqrt( (1.0 - (x/center)**2)**2 + (2*sigma*x/center)**2))
- """
- center = max(1.e-9, abs(center))
- return (amplitude/sqrt( (1.0 - (x/center)**2)**2 + (2*sigma*x/center)**2))
-
-def logistic(x, amplitude=1., center=0., sigma=1.):
- """Logistic lineshape (yet another sigmoidal curve)
- = amplitude*(1. - 1. / (1 + exp((x-center)/sigma)))
- """
- return amplitude*(1. - 1./(1. + exp((x-center)/sigma)))
-
-def lognormal(x, amplitude=1.0, center=0., sigma=1):
- """log-normal function
- lognormal(x, center, sigma)
- = (amplitude/x) * exp(-(ln(x) - center)/ (2* sigma**2))
- """
- x[where(x<=1.e-19)] = 1.e-19
- return (amplitude/(x*sigma*s2pi)) * exp(-(log(x)-center)**2/ (2* sigma**2))
-
-def students_t(x, amplitude=1.0, center=0.0, sigma=1.0):
- """Student's t distribution:
- gamma((sigma+1)/2) (1 + (x-center)**2/sigma)^(-(sigma+1)/2)
- = -------------------------
- sqrt(sigma*pi)gamma(sigma/2)
-
- """
- s1 = (sigma+1)/2.0
- denom = (sqrt(sigma*pi)*gamfcn(sigma/2))
- return amplitude*(1 + (x-center)**2/sigma)**(-s1) * gamfcn(s1) / denom
-
-
-def expgaussian(x, amplitude=1, center=0, sigma=1.0, gamma=1.0):
- """exponentially modified Gaussian
-
- = (gamma/2) exp[center*gamma + (gamma*sigma)**2/2 - gamma*x] *
- erfc[(center + gamma*sigma**2 - x)/(sqrt(2)*sigma)]
-
- http://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution
- """
- gss = gamma*sigma*sigma
- arg1 = gamma*(center +gss/2.0 - x)
- arg2 = (center + gss - x)/(s2*sigma)
- return amplitude*(gamma/2) * exp(arg1) * erfc(arg2)
-
-def donaich(x, amplitude=1.0, center=0, sigma=1.0, gamma=0.0):
- """Doniach Sunjic asymmetric lineshape, used for photo-emission
-
- = amplitude* cos(pi*gamma/2 + (1-gamma) arctan((x-center)/sigma) /
- (sigma**2 + (x-center)**2)**[(1-gamma)/2]
-
- see http://www.casaxps.com/help_manual/line_shapes.htm
- """
- arg = (x-center)/sigma
- gm1 = (1.0 - gamma)
- scale = amplitude/(sigma**gm1)
- return scale*cos(pi*gamma/2 + gm1*arctan(arg))/(1 + arg**2)**(gm1/2)
-
-def skewed_gaussian(x, amplitude=1.0, center=0.0, sigma=1.0, gamma=0.0):
- """Gaussian, skewed with error function, equal to
-
- gaussian(x, center, sigma)*(1+erf(beta*(x-center)))
-
- with beta = gamma/(sigma*sqrt(2))
-
- with gamma < 0: tail to low value of centroid
- gamma > 0: tail to high value of centroid
-
- see http://en.wikipedia.org/wiki/Skew_normal_distribution
- """
- asym = 1 + erf(gamma*(x-center)/(s2*sigma))
- return asym * gaussian(x, amplitude, center, sigma)
-
-def skewed_voigt(x, amplitude=1.0, center=0.0, sigma=1.0, gamma=None, skew=0.0):
- """Skewed Voigt lineshape, skewed with error function
- useful for ad-hoc Compton scatter profile
-
- with beta = skew/(sigma*sqrt(2))
- = voigt(x, center, sigma, gamma)*(1+erf(beta*(x-center)))
-
- skew < 0: tail to low value of centroid
- skew > 0: tail to high value of centroid
-
- see http://en.wikipedia.org/wiki/Skew_normal_distribution
- """
- beta = skew/(s2*sigma)
- asym = 1 + erf(beta*(x-center))
- return asym * voigt(x, amplitude, center, sigma, gamma=gamma)
-
-def step(x, amplitude=1.0, center=0.0, sigma=1.0, form='linear'):
- """step function:
- starts at 0.0, ends at amplitude, with half-max at center, and
- rising with form:
- 'linear' (default) = amplitude * min(1, max(0, arg))
- 'atan', 'arctan' = amplitude * (0.5 + atan(arg)/pi)
- 'erf' = amplitude * (1 + erf(arg))/2.0
- 'logistic' = amplitude * [1 - 1/(1 + exp(arg))]
-
- where arg = (x - center)/sigma
- """
- if abs(sigma) < 1.e-13:
- sigma = 1.e-13
-
- out = (x - center)/sigma
- if form == 'erf':
- out = 0.5*(1 + erf(out))
- elif form.startswith('logi'):
- out = (1. - 1./(1. + exp(out)))
- elif form in ('atan', 'arctan'):
- out = 0.5 + arctan(out)/pi
- else:
- out[where(out < 0)] = 0.0
- out[where(out > 1)] = 1.0
- return amplitude*out
-
-def rectangle(x, amplitude=1.0, center1=0.0, sigma1=1.0,
- center2=1.0, sigma2=1.0, form='linear'):
- """rectangle function: step up, step down (see step function)
- starts at 0.0, rises to amplitude (at center1 with width sigma1)
- then drops to 0.0 (at center2 with width sigma2) with form:
- 'linear' (default) = ramp_up + ramp_down
- 'atan', 'arctan' = amplitude*(atan(arg1) + atan(arg2))/pi
- 'erf' = amplitude*(erf(arg1) + erf(arg2))/2.
- 'logisitic' = amplitude*[1 - 1/(1 + exp(arg1)) - 1/(1+exp(arg2))]
-
- where arg1 = (x - center1)/sigma1
- and arg2 = -(x - center2)/sigma2
- """
- if abs(sigma1) < 1.e-13:
- sigma1 = 1.e-13
- if abs(sigma2) < 1.e-13:
- sigma2 = 1.e-13
-
- arg1 = (x - center1)/sigma1
- arg2 = (center2 - x)/sigma2
- if form == 'erf':
- out = 0.5*(erf(arg1) + erf(arg2))
- elif form.startswith('logi'):
- out = (1. - 1./(1. + exp(arg1)) - 1./(1. + exp(arg2)))
- elif form in ('atan', 'arctan'):
- out = (arctan(arg1) + arctan(arg2))/pi
- else:
- arg1[where(arg1 < 0)] = 0.0
- arg1[where(arg1 > 1)] = 1.0
- arg2[where(arg2 > 0)] = 0.0
- arg2[where(arg2 < -1)] = -1.0
- out = arg1 + arg2
- return amplitude*out
-
-def _erf(x):
- """error function. = 2/sqrt(pi)*integral(exp(-t**2), t=[0, z])"""
- return erf(x)
-
-def _erfc(x):
- """complented error function. = 1 - erf(x)"""
- return erfc(x)
-
-def _wofz(x):
- """fadeeva function for complex argument. = exp(-x**2)*erfc(-i*x)"""
- return wofz(x)
-
-def _gamma(x):
- """gamma function"""
- return gamfcn(x)
-
-def _gammaln(x):
- """log of absolute value of gamma function"""
- return gammaln(x)
-
-
-def exponential(x, amplitude=1, decay=1):
- "x -> amplitude * exp(-x/decay)"
- return amplitude * exp(-x/decay)
-
-
-def powerlaw(x, amplitude=1, exponent=1.0):
- "x -> amplitude * x**exponent"
- return amplitude * x**exponent
-
-
-def linear(x, slope, intercept):
- "x -> slope * x + intercept"
- return slope * x + intercept
-
-
-def parabolic(x, a, b, c):
- "x -> a * x**2 + b * x + c"
- return a * x**2 + b * x + c
-
-
-def assert_results_close(actual, desired, rtol=1e-03, atol=1e-03,
- err_msg='', verbose=True):
- """returns whether all parameter values in actual are close to
- those in desired"""
- for param_name, value in desired.items():
- assert_allclose(actual[param_name], value, rtol,
- atol, err_msg, verbose)
+#!/usr/bin/env python
+"""
+basic model line shapes and distribution functions
+"""
+from __future__ import division
+from numpy import (pi, log, exp, sqrt, arctan, cos, where)
+from numpy.testing import assert_allclose
+
+from scipy.special import gamma as gamfcn
+from scipy.special import gammaln, erf, erfc, wofz
+
+log2 = log(2)
+s2pi = sqrt(2*pi)
+spi = sqrt(pi)
+s2 = sqrt(2.0)
+
+functions = ('gaussian', 'lorentzian', 'voigt', 'pvoigt', 'moffat', 'pearson7',
+ 'breit_wigner', 'damped_oscillator', 'logistic', 'lognormal',
+ 'students_t', 'expgaussian', 'donaich', 'skewed_gaussian',
+ 'skewed_voigt', 'step', 'rectangle', 'erf', 'erfc', 'wofz',
+ 'gamma', 'gammaln', 'exponential', 'powerlaw', 'linear',
+ 'parabolic')
+
+def gaussian(x, amplitude=1.0, center=0.0, sigma=1.0):
+ """1 dimensional gaussian:
+ gaussian(x, amplitude, center, sigma)
+ """
+ return (amplitude/(s2pi*sigma)) * exp(-(1.0*x-center)**2 /(2*sigma**2))
+
+def lorentzian(x, amplitude=1.0, center=0.0, sigma=1.0):
+ """1 dimensional lorentzian
+ lorentzian(x, amplitude, center, sigma)
+ """
+ return (amplitude/(1 + ((1.0*x-center)/sigma)**2) ) / (pi*sigma)
+
+def voigt(x, amplitude=1.0, center=0.0, sigma=1.0, gamma=None):
+ """1 dimensional voigt function.
+ see http://en.wikipedia.org/wiki/Voigt_profile
+ """
+ if gamma is None:
+ gamma = sigma
+ z = (x-center + 1j*gamma)/ (sigma*s2)
+ return amplitude*wofz(z).real / (sigma*s2pi)
+
+def pvoigt(x, amplitude=1.0, center=0.0, sigma=1.0, fraction=0.5):
+ """1 dimensional pseudo-voigt:
+ pvoigt(x, amplitude, center, sigma, fraction)
+ = amplitude*(1-fraction)*gaussion(x, center, sigma_g) +
+ amplitude*fraction*lorentzian(x, center, sigma)
+
+ where sigma_g (the sigma for the Gaussian component) is
+
+ sigma_g = sigma / sqrt(2*log(2)) ~= sigma / 1.17741
+
+ so that the Gaussian and Lorentzian components have the
+ same FWHM of 2*sigma.
+ """
+ sigma_g = sigma / sqrt(2*log2)
+ return ((1-fraction)*gaussian(x, amplitude, center, sigma_g) +
+ fraction*lorentzian(x, amplitude, center, sigma))
+
+def moffat(x, amplitude=1, center=0., sigma=1, beta=1.):
+ """ 1 dimensional moffat function:
+
+ moffat(amplitude, center, sigma, beta) = amplitude / (((x - center)/sigma)**2 + 1)**beta
+ """
+ return amplitude / (((x - center)/sigma)**2 + 1)**beta
+
+def pearson7(x, amplitude=1.0, center=0.0, sigma=1.0, expon=1.0):
+ """pearson7 lineshape, using the wikipedia definition:
+
+ pearson7(x, center, sigma, expon) =
+ amplitude*(1+arg**2)**(-expon)/(sigma*beta(expon-0.5, 0.5))
+
+ where arg = (x-center)/sigma
+ and beta() is the beta function.
+ """
+ arg = (x-center)/sigma
+ scale = amplitude * gamfcn(expon)/(gamfcn(0.5)*gamfcn(expon-0.5))
+ return scale*(1+arg**2)**(-expon)/sigma
+
+def breit_wigner(x, amplitude=1.0, center=0.0, sigma=1.0, q=1.0):
+ """Breit-Wigner-Fano lineshape:
+ = amplitude*(q*sigma/2 + x - center)**2 / ( (sigma/2)**2 + (x - center)**2 )
+ """
+ gam = sigma/2.0
+ return amplitude*(q*gam + x - center)**2 / (gam*gam + (x-center)**2)
+
+def damped_oscillator(x, amplitude=1.0, center=1., sigma=0.1):
+ """amplitude for a damped harmonic oscillator
+ amplitude/sqrt( (1.0 - (x/center)**2)**2 + (2*sigma*x/center)**2))
+ """
+ center = max(1.e-9, abs(center))
+ return (amplitude/sqrt( (1.0 - (x/center)**2)**2 + (2*sigma*x/center)**2))
+
+def logistic(x, amplitude=1., center=0., sigma=1.):
+ """Logistic lineshape (yet another sigmoidal curve)
+ = amplitude*(1. - 1. / (1 + exp((x-center)/sigma)))
+ """
+ return amplitude*(1. - 1./(1. + exp((x-center)/sigma)))
+
+def lognormal(x, amplitude=1.0, center=0., sigma=1):
+ """log-normal function
+ lognormal(x, center, sigma)
+ = (amplitude/x) * exp(-(ln(x) - center)/ (2* sigma**2))
+ """
+ x[where(x<=1.e-19)] = 1.e-19
+ return (amplitude/(x*sigma*s2pi)) * exp(-(log(x)-center)**2/ (2* sigma**2))
+
+def students_t(x, amplitude=1.0, center=0.0, sigma=1.0):
+ """Student's t distribution:
+ gamma((sigma+1)/2) (1 + (x-center)**2/sigma)^(-(sigma+1)/2)
+ = -------------------------
+ sqrt(sigma*pi)gamma(sigma/2)
+
+ """
+ s1 = (sigma+1)/2.0
+ denom = (sqrt(sigma*pi)*gamfcn(sigma/2))
+ return amplitude*(1 + (x-center)**2/sigma)**(-s1) * gamfcn(s1) / denom
+
+
+def expgaussian(x, amplitude=1, center=0, sigma=1.0, gamma=1.0):
+ """exponentially modified Gaussian
+
+ = (gamma/2) exp[center*gamma + (gamma*sigma)**2/2 - gamma*x] *
+ erfc[(center + gamma*sigma**2 - x)/(sqrt(2)*sigma)]
+
+ http://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution
+ """
+ gss = gamma*sigma*sigma
+ arg1 = gamma*(center +gss/2.0 - x)
+ arg2 = (center + gss - x)/(s2*sigma)
+ return amplitude*(gamma/2) * exp(arg1) * erfc(arg2)
+
+def donaich(x, amplitude=1.0, center=0, sigma=1.0, gamma=0.0):
+ """Doniach Sunjic asymmetric lineshape, used for photo-emission
+
+ = amplitude* cos(pi*gamma/2 + (1-gamma) arctan((x-center)/sigma) /
+ (sigma**2 + (x-center)**2)**[(1-gamma)/2]
+
+ see http://www.casaxps.com/help_manual/line_shapes.htm
+ """
+ arg = (x-center)/sigma
+ gm1 = (1.0 - gamma)
+ scale = amplitude/(sigma**gm1)
+ return scale*cos(pi*gamma/2 + gm1*arctan(arg))/(1 + arg**2)**(gm1/2)
+
+def skewed_gaussian(x, amplitude=1.0, center=0.0, sigma=1.0, gamma=0.0):
+ """Gaussian, skewed with error function, equal to
+
+ gaussian(x, center, sigma)*(1+erf(beta*(x-center)))
+
+ with beta = gamma/(sigma*sqrt(2))
+
+ with gamma < 0: tail to low value of centroid
+ gamma > 0: tail to high value of centroid
+
+ see http://en.wikipedia.org/wiki/Skew_normal_distribution
+ """
+ asym = 1 + erf(gamma*(x-center)/(s2*sigma))
+ return asym * gaussian(x, amplitude, center, sigma)
+
+def skewed_voigt(x, amplitude=1.0, center=0.0, sigma=1.0, gamma=None, skew=0.0):
+ """Skewed Voigt lineshape, skewed with error function
+ useful for ad-hoc Compton scatter profile
+
+ with beta = skew/(sigma*sqrt(2))
+ = voigt(x, center, sigma, gamma)*(1+erf(beta*(x-center)))
+
+ skew < 0: tail to low value of centroid
+ skew > 0: tail to high value of centroid
+
+ see http://en.wikipedia.org/wiki/Skew_normal_distribution
+ """
+ beta = skew/(s2*sigma)
+ asym = 1 + erf(beta*(x-center))
+ return asym * voigt(x, amplitude, center, sigma, gamma=gamma)
+
+def step(x, amplitude=1.0, center=0.0, sigma=1.0, form='linear'):
+ """step function:
+ starts at 0.0, ends at amplitude, with half-max at center, and
+ rising with form:
+ 'linear' (default) = amplitude * min(1, max(0, arg))
+ 'atan', 'arctan' = amplitude * (0.5 + atan(arg)/pi)
+ 'erf' = amplitude * (1 + erf(arg))/2.0
+ 'logistic' = amplitude * [1 - 1/(1 + exp(arg))]
+
+ where arg = (x - center)/sigma
+ """
+ if abs(sigma) < 1.e-13:
+ sigma = 1.e-13
+
+ out = (x - center)/sigma
+ if form == 'erf':
+ out = 0.5*(1 + erf(out))
+ elif form.startswith('logi'):
+ out = (1. - 1./(1. + exp(out)))
+ elif form in ('atan', 'arctan'):
+ out = 0.5 + arctan(out)/pi
+ else:
+ out[where(out < 0)] = 0.0
+ out[where(out > 1)] = 1.0
+ return amplitude*out
+
+def rectangle(x, amplitude=1.0, center1=0.0, sigma1=1.0,
+ center2=1.0, sigma2=1.0, form='linear'):
+ """rectangle function: step up, step down (see step function)
+ starts at 0.0, rises to amplitude (at center1 with width sigma1)
+ then drops to 0.0 (at center2 with width sigma2) with form:
+ 'linear' (default) = ramp_up + ramp_down
+ 'atan', 'arctan' = amplitude*(atan(arg1) + atan(arg2))/pi
+ 'erf' = amplitude*(erf(arg1) + erf(arg2))/2.
+ 'logisitic' = amplitude*[1 - 1/(1 + exp(arg1)) - 1/(1+exp(arg2))]
+
+ where arg1 = (x - center1)/sigma1
+ and arg2 = -(x - center2)/sigma2
+ """
+ if abs(sigma1) < 1.e-13:
+ sigma1 = 1.e-13
+ if abs(sigma2) < 1.e-13:
+ sigma2 = 1.e-13
+
+ arg1 = (x - center1)/sigma1
+ arg2 = (center2 - x)/sigma2
+ if form == 'erf':
+ out = 0.5*(erf(arg1) + erf(arg2))
+ elif form.startswith('logi'):
+ out = (1. - 1./(1. + exp(arg1)) - 1./(1. + exp(arg2)))
+ elif form in ('atan', 'arctan'):
+ out = (arctan(arg1) + arctan(arg2))/pi
+ else:
+ arg1[where(arg1 < 0)] = 0.0
+ arg1[where(arg1 > 1)] = 1.0
+ arg2[where(arg2 > 0)] = 0.0
+ arg2[where(arg2 < -1)] = -1.0
+ out = arg1 + arg2
+ return amplitude*out
+
+def _erf(x):
+ """error function. = 2/sqrt(pi)*integral(exp(-t**2), t=[0, z])"""
+ return erf(x)
+
+def _erfc(x):
+ """complented error function. = 1 - erf(x)"""
+ return erfc(x)
+
+def _wofz(x):
+ """fadeeva function for complex argument. = exp(-x**2)*erfc(-i*x)"""
+ return wofz(x)
+
+def _gamma(x):
+ """gamma function"""
+ return gamfcn(x)
+
+def _gammaln(x):
+ """log of absolute value of gamma function"""
+ return gammaln(x)
+
+
+def exponential(x, amplitude=1, decay=1):
+ "x -> amplitude * exp(-x/decay)"
+ return amplitude * exp(-x/decay)
+
+
+def powerlaw(x, amplitude=1, exponent=1.0):
+ "x -> amplitude * x**exponent"
+ return amplitude * x**exponent
+
+
+def linear(x, slope, intercept):
+ "x -> slope * x + intercept"
+ return slope * x + intercept
+
+
+def parabolic(x, a, b, c):
+ "x -> a * x**2 + b * x + c"
+ return a * x**2 + b * x + c
+
+
+def assert_results_close(actual, desired, rtol=1e-03, atol=1e-03,
+ err_msg='', verbose=True):
+ """returns whether all parameter values in actual are close to
+ those in desired"""
+ for param_name, value in desired.items():
+ assert_allclose(actual[param_name], value, rtol,
+ atol, err_msg, verbose)
diff --git a/lmfit/minimizer.py b/lmfit/minimizer.py
index 7fca545..c67a396 100644
--- a/lmfit/minimizer.py
+++ b/lmfit/minimizer.py
@@ -1,774 +1,1282 @@
-"""
-Simple minimizer is a wrapper around scipy.leastsq, allowing a
-user to build a fitting model as a function of general purpose
-Fit Parameters that can be fixed or floated, bounded, and written
-as a simple expression of other Fit Parameters.
-
-The user sets up a model in terms of instance of Parameters, writes a
-function-to-be-minimized (residual function) in terms of these Parameters.
-
- Copyright (c) 2011 Matthew Newville, The University of Chicago
- <newville at cars.uchicago.edu>
-"""
-
-from copy import deepcopy
-import numpy as np
-from numpy import (dot, eye, ndarray, ones_like,
- sqrt, take, transpose, triu, deprecate)
-from numpy.dual import inv
-from numpy.linalg import LinAlgError
-
-from scipy.optimize import leastsq as scipy_leastsq
-from scipy.optimize import fmin as scipy_fmin
-from scipy.optimize.lbfgsb import fmin_l_bfgs_b as scipy_lbfgsb
-
-# differential_evolution is only present in scipy >= 0.15
-try:
- from scipy.optimize import differential_evolution as scipy_diffev
-except ImportError:
- from ._differentialevolution import differential_evolution as scipy_diffev
-
-# check for scipy.optimize.minimize
-HAS_SCALAR_MIN = False
-try:
- from scipy.optimize import minimize as scipy_minimize
- HAS_SCALAR_MIN = True
-except ImportError:
- pass
-
-from .asteval import Interpreter
-from .parameter import Parameter, Parameters
-
-# use locally modified version of uncertainties package
-from . import uncertainties
-
-
-def asteval_with_uncertainties(*vals, **kwargs):
- """
- given values for variables, calculate object value.
- This is used by the uncertainties package to calculate
- the uncertainty in an object even with a complicated
- expression.
- """
- _obj = kwargs.get('_obj', None)
- _pars = kwargs.get('_pars', None)
- _names = kwargs.get('_names', None)
- _asteval = _pars._asteval
- if (_obj is None or _pars is None or _names is None or
- _asteval is None or _obj._expr_ast is None):
- return 0
- for val, name in zip(vals, _names):
- _asteval.symtable[name] = val
- return _asteval.eval(_obj._expr_ast)
-
-wrap_ueval = uncertainties.wrap(asteval_with_uncertainties)
-
-def eval_stderr(obj, uvars, _names, _pars):
- """evaluate uncertainty and set .stderr for a parameter `obj`
- given the uncertain values `uvars` (a list of uncertainties.ufloats),
- a list of parameter names that matches uvars, and a dict of param
- objects, keyed by name.
-
- This uses the uncertainties package wrapped function to evaluate the
- uncertainty for an arbitrary expression (in obj._expr_ast) of parameters.
- """
- if not isinstance(obj, Parameter) or getattr(obj, '_expr_ast', None) is None:
- return
- uval = wrap_ueval(*uvars, _obj=obj, _names=_names, _pars=_pars)
- try:
- obj.stderr = uval.std_dev()
- except:
- obj.stderr = 0
-
-
-class MinimizerException(Exception):
- """General Purpose Exception"""
- def __init__(self, msg):
- Exception.__init__(self)
- self.msg = msg
-
- def __str__(self):
- return "\n%s" % (self.msg)
-
-
-def _differential_evolution(func, x0, **kwds):
- """
- A wrapper for differential_evolution that can be used with scipy.minimize
- """
- kwargs = dict(args=(), strategy='best1bin', maxiter=None, popsize=15,
- tol=0.01, mutation=(0.5, 1), recombination=0.7, seed=None,
- callback=None, disp=False, polish=True,
- init='latinhypercube')
-
- for k, v in kwds.items():
- if k in kwargs:
- kwargs[k] = v
-
- return scipy_diffev(func, kwds['bounds'], **kwargs)
-
-SCALAR_METHODS = {'nelder': 'Nelder-Mead',
- 'powell': 'Powell',
- 'cg': 'CG',
- 'bfgs': 'BFGS',
- 'newton': 'Newton-CG',
- 'lbfgsb': 'L-BFGS-B',
- 'l-bfgsb':'L-BFGS-B',
- 'tnc': 'TNC',
- 'cobyla': 'COBYLA',
- 'slsqp': 'SLSQP',
- 'dogleg': 'dogleg',
- 'trust-ncg': 'trust-ncg',
- 'differential_evolution': 'differential_evolution'}
-
-
-class MinimizerResult(object):
- """ The result of a minimization.
-
- Attributes
- ----------
- params : Parameters
- The best-fit parameters
- success : bool
- Whether the minimization was successful
- status : int
- Termination status of the optimizer. Its value depends on the
- underlying solver. Refer to `message` for details.
-
- Notes
- -----
- additional attributes not listed above depending of the
- specific solver. Since this class is essentially a subclass of dict
- with attribute accessors, one can see which attributes are available
- using the `keys()` method.
- """
- def __init__(self, **kws):
- for key, val in kws.items():
- setattr(self, key, val)
-
-class Minimizer(object):
- """A general minimizer for curve fitting"""
- err_nonparam = ("params must be a minimizer.Parameters() instance or list "
- "of Parameters()")
- err_maxfev = ("Too many function calls (max set to %i)! Use:"
- " minimize(func, params, ..., maxfev=NNN)"
- "or set leastsq_kws['maxfev'] to increase this maximum.")
-
- def __init__(self, userfcn, params, fcn_args=None, fcn_kws=None,
- iter_cb=None, scale_covar=True, **kws):
- """
- Initialization of the Minimzer class
-
- Parameters
- ----------
- userfcn : callable
- objective function that returns the residual (difference between
- model and data) to be minimized in a least squares sense. The
- function must have the signature:
- `userfcn(params, *fcn_args, **fcn_kws)`
- params : lmfit.parameter.Parameters object.
- contains the Parameters for the model.
- fcn_args : tuple, optional
- positional arguments to pass to userfcn.
- fcn_kws : dict, optional
- keyword arguments to pass to userfcn.
- iter_cb : callable, optional
- Function to be called at each fit iteration. This function should
- have the signature:
- `iter_cb(params, iter, resid, *fcn_args, **fcn_kws)`,
- where where `params` will have the current parameter values, `iter`
- the iteration, `resid` the current residual array, and `*fcn_args`
- and `**fcn_kws` as passed to the objective function.
- scale_covar : bool, optional
- Whether to automatically scale the covariance matrix (leastsq
- only).
- kws : dict, optional
- Options to pass to the minimizer being used.
-
- Notes
- -----
- The objective function should return the value to be minimized. For the
- Levenberg-Marquardt algorithm from leastsq(), this returned value must
- be an array, with a length greater than or equal to the number of
- fitting variables in the model. For the other methods, the return value
- can either be a scalar or an array. If an array is returned, the sum of
- squares of the array will be sent to the underlying fitting method,
- effectively doing a least-squares optimization of the return values.
-
- A common use for the fcn_args and fcn_kwds would be to pass in other
- data needed to calculate the residual, including such things as the
- data array, dependent variable, uncertainties in the data, and other
- data structures for the model calculation.
- """
- self.userfcn = userfcn
- self.userargs = fcn_args
- if self.userargs is None:
- self.userargs = []
-
- self.userkws = fcn_kws
- if self.userkws is None:
- self.userkws = {}
- self.kws = kws
- self.iter_cb = iter_cb
- self.scale_covar = scale_covar
- self.nfev = 0
- self.nfree = 0
- self.ndata = 0
- self.ier = 0
- self._abort = False
- self.success = True
- self.errorbars = False
- self.message = None
- self.lmdif_message = None
- self.chisqr = None
- self.redchi = None
- self.covar = None
- self.residual = None
-
- self.params = params
- self.jacfcn = None
-
- @property
- def values(self):
- """
- Returns
- -------
- param_values : dict
- Parameter values in a simple dictionary.
- """
-
- return dict([(name, p.value) for name, p in self.result.params.items()])
-
- def __residual(self, fvars):
- """
- Residual function used for least-squares fit.
- With the new, candidate values of fvars (the fitting variables), this
- evaluates all parameters, including setting bounds and evaluating
- constraints, and then passes those to the user-supplied function to
- calculate the residual.
- """
- # set parameter values
- if self._abort:
- return None
- params = self.result.params
- for name, val in zip(self.result.var_names, fvars):
- params[name].value = params[name].from_internal(val)
- self.result.nfev = self.result.nfev + 1
-
- params.update_constraints()
- out = self.userfcn(params, *self.userargs, **self.userkws)
- if callable(self.iter_cb):
- abort = self.iter_cb(params, self.result.nfev, out,
- *self.userargs, **self.userkws)
- self._abort = self._abort or abort
- if not self._abort:
- return np.asarray(out).ravel()
-
- def __jacobian(self, fvars):
- """
- analytical jacobian to be used with the Levenberg-Marquardt
-
- modified 02-01-2012 by Glenn Jones, Aberystwyth University
- modified 06-29-2015 M Newville to apply gradient scaling
- for bounded variables (thanks to JJ Helmus, N Mayorov)
- """
- pars = self.result.params
- grad_scale = ones_like(fvars)
- for ivar, name in enumerate(self.result.var_names):
- val = fvars[ivar]
- pars[name].value = pars[name].from_internal(val)
- grad_scale[ivar] = pars[name].scale_gradient(val)
-
- self.result.nfev = self.result.nfev + 1
- pars.update_constraints()
- # compute the jacobian for "internal" unbounded variables,
- # the rescale for bounded "external" variables.
- jac = self.jacfcn(pars, *self.userargs, **self.userkws)
- if self.col_deriv:
- jac = (jac.transpose()*grad_scale).transpose()
- else:
- jac = jac*grad_scale
- return jac
-
- def penalty(self, fvars):
- """
- Penalty function for scalar minimizers:
-
- Parameters
- ----------
- fvars : array of values for the variable parameters
-
- Returns
- -------
- r - float
- The user evaluated user-supplied objective function. If the
- objective function is an array, return the array sum-of-squares
- """
- r = self.__residual(fvars)
- if isinstance(r, ndarray):
- r = (r*r).sum()
- return r
-
- def prepare_fit(self, params=None):
- """
- Prepares parameters for fitting,
- return array of initial values
- """
- # determine which parameters are actually variables
- # and which are defined expressions.
- result = self.result = MinimizerResult()
- if params is not None:
- self.params = params
- if isinstance(self.params, Parameters):
- result.params = deepcopy(self.params)
- elif isinstance(self.params, (list, tuple)):
- result.params = Parameters()
- for par in self.params:
- if not isinstance(par, Parameter):
- raise MinimizerException(self.err_nonparam)
- else:
- result.params[par.name] = par
- elif self.params is None:
- raise MinimizerException(self.err_nonparam)
-
- # determine which parameters are actually variables
- # and which are defined expressions.
-
- result.var_names = [] # note that this *does* belong to self...
- result.init_vals = []
- result.params.update_constraints()
- result.nfev = 0
- result.errorbars = False
- result.aborted = False
- for name, par in self.result.params.items():
- par.stderr = None
- par.correl = None
- if par.expr is not None:
- par.vary = False
- if par.vary:
- result.var_names.append(name)
- result.init_vals.append(par.setup_bounds())
-
- par.init_value = par.value
- if par.name is None:
- par.name = name
- result.nvarys = len(result.var_names)
- return result
-
- def unprepare_fit(self):
- """
- Unprepares the fit, so that subsequent fits will be
- forced to run prepare_fit.
-
- removes ast compilations of constraint expressions
- """
- pass
-
- @deprecate(message=' Deprecated in lmfit 0.8.2, use scalar_minimize '
- 'and method=\'L-BFGS-B\' instead')
- def lbfgsb(self, **kws):
- """
- Use l-bfgs-b minimization
-
- Parameters
- ----------
- kws : dict
- Minimizer options to pass to the
- scipy.optimize.lbfgsb.fmin_l_bfgs_b function.
-
- """
- raise NotImplementedError("use scalar_minimize(method='L-BFGS-B')")
-
-
- @deprecate(message=' Deprecated in lmfit 0.8.2, use scalar_minimize '
- 'and method=\'Nelder-Mead\' instead')
- def fmin(self, **kws):
- """
- Use Nelder-Mead (simplex) minimization
-
- Parameters
- ----------
- kws : dict
- Minimizer options to pass to the scipy.optimize.fmin minimizer.
- """
- raise NotImplementedError("use scalar_minimize(method='Nelder-Mead')")
-
- def scalar_minimize(self, method='Nelder-Mead', params=None, **kws):
- """
- Use one of the scalar minimization methods from
- scipy.optimize.minimize.
-
- Parameters
- ----------
- method : str, optional
- Name of the fitting method to use.
- One of:
- 'Nelder-Mead' (default)
- 'L-BFGS-B'
- 'Powell'
- 'CG'
- 'Newton-CG'
- 'COBYLA'
- 'TNC'
- 'trust-ncg'
- 'dogleg'
- 'SLSQP'
- 'differential_evolution'
-
- params : Parameters, optional
- Parameters to use as starting points.
- kws : dict, optional
- Minimizer options pass to scipy.optimize.minimize.
-
- If the objective function returns a numpy array instead
- of the expected scalar, the sum of squares of the array
- will be used.
-
- Note that bounds and constraints can be set on Parameters
- for any of these methods, so are not supported separately
- for those designed to use bounds. However, if you use the
- differential_evolution option you must specify finite
- (min, max) for each Parameter.
-
- Returns
- -------
- success : bool
- Whether the fit was successful.
-
- """
- if not HAS_SCALAR_MIN:
- raise NotImplementedError
-
- result = self.prepare_fit(params=params)
- vars = result.init_vals
- params = result.params
-
- fmin_kws = dict(method=method,
- options={'maxiter': 1000 * (len(vars) + 1)})
- fmin_kws.update(self.kws)
- fmin_kws.update(kws)
-
- # hess supported only in some methods
- if 'hess' in fmin_kws and method not in ('Newton-CG',
- 'dogleg', 'trust-ncg'):
- fmin_kws.pop('hess')
-
- # jac supported only in some methods (and Dfun could be used...)
- if 'jac' not in fmin_kws and fmin_kws.get('Dfun', None) is not None:
- self.jacfcn = fmin_kws.pop('jac')
- fmin_kws['jac'] = self.__jacobian
-
- if 'jac' in fmin_kws and method not in ('CG', 'BFGS', 'Newton-CG',
- 'dogleg', 'trust-ncg'):
- self.jacfcn = None
- fmin_kws.pop('jac')
-
- if method == 'differential_evolution':
- fmin_kws['method'] = _differential_evolution
- bounds = [(par.min, par.max) for par in params.values()]
- if not np.all(np.isfinite(bounds)):
- raise ValueError('With differential evolution finite bounds '
- 'are required for each parameter')
- bounds = [(-np.pi / 2., np.pi / 2.)] * len(vars)
- fmin_kws['bounds'] = bounds
-
- # in scipy 0.14 this can be called directly from scipy_minimize
- # When minimum scipy is 0.14 the following line and the else
- # can be removed.
- ret = _differential_evolution(self.penalty, vars, **fmin_kws)
- else:
- ret = scipy_minimize(self.penalty, vars, **fmin_kws)
-
- result.aborted = self._abort
- self._abort = False
-
- for attr in dir(ret):
- if not attr.startswith('_'):
- setattr(result, attr, getattr(ret, attr))
-
- result.chisqr = result.residual = self.__residual(ret.x)
- result.nvarys = len(vars)
- result.ndata = 1
- result.nfree = 1
- if isinstance(result.residual, ndarray):
- result.chisqr = (result.chisqr**2).sum()
- result.ndata = len(result.residual)
- result.nfree = result.ndata - result.nvarys
- result.redchi = result.chisqr / result.nfree
- _log_likelihood = result.ndata * np.log(result.redchi)
- result.aic = _log_likelihood + 2 * result.nvarys
- result.bic = _log_likelihood + np.log(result.ndata) * result.nvarys
-
- return result
-
- def leastsq(self, params=None, **kws):
- """
- Use Levenberg-Marquardt minimization to perform a fit.
- This assumes that ModelParameters have been stored, and a function to
- minimize has been properly set up.
-
- This wraps scipy.optimize.leastsq.
-
- When possible, this calculates the estimated uncertainties and
- variable correlations from the covariance matrix.
-
- Writes outputs to many internal attributes.
-
- Parameters
- ----------
- params : Parameters, optional
- Parameters to use as starting points.
- kws : dict, optional
- Minimizer options to pass to scipy.optimize.leastsq.
-
- Returns
- -------
- success : bool
- True if fit was successful, False if not.
- """
- result = self.prepare_fit(params=params)
- vars = result.init_vals
- nvars = len(vars)
- lskws = dict(full_output=1, xtol=1.e-7, ftol=1.e-7, col_deriv=False,
- gtol=1.e-7, maxfev=2000*(nvars+1), Dfun=None)
-
- lskws.update(self.kws)
- lskws.update(kws)
-
- self.col_deriv = False
- if lskws['Dfun'] is not None:
- self.jacfcn = lskws['Dfun']
- self.col_deriv = lskws['col_deriv']
- lskws['Dfun'] = self.__jacobian
-
- # suppress runtime warnings during fit and error analysis
- orig_warn_settings = np.geterr()
- np.seterr(all='ignore')
-
- lsout = scipy_leastsq(self.__residual, vars, **lskws)
- _best, _cov, infodict, errmsg, ier = lsout
- result.aborted = self._abort
- self._abort = False
-
- result.residual = resid = infodict['fvec']
- result.ier = ier
- result.lmdif_message = errmsg
- result.message = 'Fit succeeded.'
- result.success = ier in [1, 2, 3, 4]
- if result.aborted:
- result.message = 'Fit aborted by user callback.'
- result.success = False
- elif ier == 0:
- result.message = 'Invalid Input Parameters.'
- elif ier == 5:
- result.message = self.err_maxfev % lskws['maxfev']
- else:
- result.message = 'Tolerance seems to be too small.'
-
- result.ndata = len(resid)
-
- result.chisqr = (resid**2).sum()
- result.nfree = (result.ndata - nvars)
- result.redchi = result.chisqr / result.nfree
- _log_likelihood = result.ndata * np.log(result.redchi)
- result.aic = _log_likelihood + 2 * nvars
- result.bic = _log_likelihood + np.log(result.ndata) * nvars
-
- params = result.params
-
- # need to map _best values to params, then calculate the
- # grad for the variable parameters
- grad = ones_like(_best)
- vbest = ones_like(_best)
-
- # ensure that _best, vbest, and grad are not
- # broken 1-element ndarrays.
- if len(np.shape(_best)) == 0:
- _best = np.array([_best])
- if len(np.shape(vbest)) == 0:
- vbest = np.array([vbest])
- if len(np.shape(grad)) == 0:
- grad = np.array([grad])
-
- for ivar, name in enumerate(result.var_names):
- grad[ivar] = params[name].scale_gradient(_best[ivar])
- vbest[ivar] = params[name].value
-
- # modified from JJ Helmus' leastsqbound.py
- infodict['fjac'] = transpose(transpose(infodict['fjac']) /
- take(grad, infodict['ipvt'] - 1))
- rvec = dot(triu(transpose(infodict['fjac'])[:nvars, :]),
- take(eye(nvars), infodict['ipvt'] - 1, 0))
- try:
- result.covar = inv(dot(transpose(rvec), rvec))
- except (LinAlgError, ValueError):
- result.covar = None
-
- has_expr = False
- for par in params.values():
- par.stderr, par.correl = 0, None
- has_expr = has_expr or par.expr is not None
-
- # self.errorbars = error bars were successfully estimated
- result.errorbars = (result.covar is not None)
- if result.aborted:
- result.errorbars = False
- if result.errorbars:
- if self.scale_covar:
- result.covar *= result.redchi
- for ivar, name in enumerate(result.var_names):
- par = params[name]
- par.stderr = sqrt(result.covar[ivar, ivar])
- par.correl = {}
- try:
- result.errorbars = result.errorbars and (par.stderr > 0.0)
- for jvar, varn2 in enumerate(result.var_names):
- if jvar != ivar:
- par.correl[varn2] = (result.covar[ivar, jvar] /
- (par.stderr * sqrt(result.covar[jvar, jvar])))
- except:
- result.errorbars = False
-
- uvars = None
- if has_expr:
- # uncertainties on constrained parameters:
- # get values with uncertainties (including correlations),
- # temporarily set Parameter values to these,
- # re-evaluate contrained parameters to extract stderr
- # and then set Parameters back to best-fit value
- try:
- uvars = uncertainties.correlated_values(vbest, result.covar)
- except (LinAlgError, ValueError):
- uvars = None
- if uvars is not None:
- for par in params.values():
- eval_stderr(par, uvars, result.var_names, params)
- # restore nominal values
- for v, nam in zip(uvars, result.var_names):
- params[nam].value = v.nominal_value
-
- if not result.errorbars:
- result.message = '%s. Could not estimate error-bars'% result.message
-
- np.seterr(**orig_warn_settings)
- return result
-
- def minimize(self, method='leastsq', params=None, **kws):
- """
- Perform the minimization.
-
- Parameters
- ----------
- method : str, optional
- Name of the fitting method to use.
- One of:
- 'leastsq' - Levenberg-Marquardt (default)
- 'nelder' - Nelder-Mead
- 'lbfgsb' - L-BFGS-B
- 'powell' - Powell
- 'cg' - Conjugate-Gradient
- 'newton' - Newton-CG
- 'cobyla' - Cobyla
- 'tnc' - Truncate Newton
- 'trust-ncg' - Trust Newton-CGn
- 'dogleg' - Dogleg
- 'slsqp' - Sequential Linear Squares Programming
- 'differential_evolution' - differential evolution
-
- params : Parameters, optional
- parameters to use as starting values
-
- Returns
- -------
- result : MinimizerResult
-
- MinimizerResult object contains updated params, fit statistics, etc.
-
- """
-
- function = self.leastsq
- kwargs = {'params': params}
- kwargs.update(kws)
-
- user_method = method.lower()
- if user_method.startswith('least'):
- function = self.leastsq
- elif HAS_SCALAR_MIN:
- function = self.scalar_minimize
- for key, val in SCALAR_METHODS.items():
- if (key.lower().startswith(user_method) or
- val.lower().startswith(user_method)):
- kwargs['method'] = val
- elif (user_method.startswith('nelder') or
- user_method.startswith('fmin')):
- function = self.fmin
- elif user_method.startswith('lbfgsb'):
- function = self.lbfgsb
- return function(**kwargs)
-
-def minimize(fcn, params, method='leastsq', args=None, kws=None,
- scale_covar=True, iter_cb=None, **fit_kws):
- """
- A general purpose curvefitting function
- The minimize function takes a objective function to be minimized, a
- dictionary (lmfit.parameter.Parameters) containing the model parameters,
- and several optional arguments.
-
- Parameters
- ----------
- fcn : callable
- objective function that returns the residual (difference between
- model and data) to be minimized in a least squares sense. The
- function must have the signature:
- `fcn(params, *args, **kws)`
- params : lmfit.parameter.Parameters object.
- contains the Parameters for the model.
- method : str, optional
- Name of the fitting method to use.
- One of:
- 'leastsq' - Levenberg-Marquardt (default)
- 'nelder' - Nelder-Mead
- 'lbfgsb' - L-BFGS-B
- 'powell' - Powell
- 'cg' - Conjugate-Gradient
- 'newton' - Newton-CG
- 'cobyla' - Cobyla
- 'tnc' - Truncate Newton
- 'trust-ncg' - Trust Newton-CGn
- 'dogleg' - Dogleg
- 'slsqp' - Sequential Linear Squares Programming
- 'differential_evolution' - differential evolution
-
- args : tuple, optional
- Positional arguments to pass to fcn.
- kws : dict, optional
- keyword arguments to pass to fcn.
- iter_cb : callable, optional
- Function to be called at each fit iteration. This function should
- have the signature `iter_cb(params, iter, resid, *args, **kws)`,
- where where `params` will have the current parameter values, `iter`
- the iteration, `resid` the current residual array, and `*args`
- and `**kws` as passed to the objective function.
- scale_covar : bool, optional
- Whether to automatically scale the covariance matrix (leastsq
- only).
- fit_kws : dict, optional
- Options to pass to the minimizer being used.
-
- Notes
- -----
- The objective function should return the value to be minimized. For the
- Levenberg-Marquardt algorithm from leastsq(), this returned value must
- be an array, with a length greater than or equal to the number of
- fitting variables in the model. For the other methods, the return value
- can either be a scalar or an array. If an array is returned, the sum of
- squares of the array will be sent to the underlying fitting method,
- effectively doing a least-squares optimization of the return values.
-
- A common use for `args` and `kwds` would be to pass in other
- data needed to calculate the residual, including such things as the
- data array, dependent variable, uncertainties in the data, and other
- data structures for the model calculation.
- """
- fitter = Minimizer(fcn, params, fcn_args=args, fcn_kws=kws,
- iter_cb=iter_cb, scale_covar=scale_covar, **fit_kws)
- return fitter.minimize(method=method)
+"""
+Simple minimizer is a wrapper around scipy.leastsq, allowing a
+user to build a fitting model as a function of general purpose
+Fit Parameters that can be fixed or floated, bounded, and written
+as a simple expression of other Fit Parameters.
+
+The user sets up a model in terms of instance of Parameters, writes a
+function-to-be-minimized (residual function) in terms of these Parameters.
+
+ Copyright (c) 2011 Matthew Newville, The University of Chicago
+ <newville at cars.uchicago.edu>
+"""
+
+from copy import deepcopy
+import numpy as np
+from numpy import (dot, eye, ndarray, ones_like,
+ sqrt, take, transpose, triu, deprecate)
+from numpy.dual import inv
+from numpy.linalg import LinAlgError
+import multiprocessing
+import numbers
+
+from scipy.optimize import leastsq as scipy_leastsq
+
+# differential_evolution is only present in scipy >= 0.15
+try:
+ from scipy.optimize import differential_evolution as scipy_diffev
+except ImportError:
+ from ._differentialevolution import differential_evolution as scipy_diffev
+
+# check for EMCEE
+HAS_EMCEE = False
+try:
+ import emcee as emcee
+ HAS_EMCEE = True
+except ImportError:
+ pass
+
+# check for pandas
+HAS_PANDAS = False
+try:
+ import pandas as pd
+ HAS_PANDAS = True
+except ImportError:
+ pass
+
+# check for scipy.optimize.minimize
+HAS_SCALAR_MIN = False
+try:
+ from scipy.optimize import minimize as scipy_minimize
+ HAS_SCALAR_MIN = True
+except ImportError:
+ pass
+
+from .parameter import Parameter, Parameters
+
+# use locally modified version of uncertainties package
+from . import uncertainties
+
+
+def asteval_with_uncertainties(*vals, **kwargs):
+ """
+ given values for variables, calculate object value.
+ This is used by the uncertainties package to calculate
+ the uncertainty in an object even with a complicated
+ expression.
+ """
+ _obj = kwargs.get('_obj', None)
+ _pars = kwargs.get('_pars', None)
+ _names = kwargs.get('_names', None)
+ _asteval = _pars._asteval
+ if (_obj is None or _pars is None or _names is None or
+ _asteval is None or _obj._expr_ast is None):
+ return 0
+ for val, name in zip(vals, _names):
+ _asteval.symtable[name] = val
+ return _asteval.eval(_obj._expr_ast)
+
+wrap_ueval = uncertainties.wrap(asteval_with_uncertainties)
+
+
+def eval_stderr(obj, uvars, _names, _pars):
+ """evaluate uncertainty and set .stderr for a parameter `obj`
+ given the uncertain values `uvars` (a list of uncertainties.ufloats),
+ a list of parameter names that matches uvars, and a dict of param
+ objects, keyed by name.
+
+ This uses the uncertainties package wrapped function to evaluate the
+ uncertainty for an arbitrary expression (in obj._expr_ast) of parameters.
+ """
+ if not isinstance(obj, Parameter) or getattr(obj, '_expr_ast', None) is None:
+ return
+ uval = wrap_ueval(*uvars, _obj=obj, _names=_names, _pars=_pars)
+ try:
+ obj.stderr = uval.std_dev()
+ except:
+ obj.stderr = 0
+
+
+class MinimizerException(Exception):
+ """General Purpose Exception"""
+ def __init__(self, msg):
+ Exception.__init__(self)
+ self.msg = msg
+
+ def __str__(self):
+ return "\n%s" % self.msg
+
+
+def _differential_evolution(func, x0, **kwds):
+ """
+ A wrapper for differential_evolution that can be used with scipy.minimize
+ """
+ kwargs = dict(args=(), strategy='best1bin', maxiter=None, popsize=15,
+ tol=0.01, mutation=(0.5, 1), recombination=0.7, seed=None,
+ callback=None, disp=False, polish=True,
+ init='latinhypercube')
+
+ for k, v in kwds.items():
+ if k in kwargs:
+ kwargs[k] = v
+
+ return scipy_diffev(func, kwds['bounds'], **kwargs)
+
+SCALAR_METHODS = {'nelder': 'Nelder-Mead',
+ 'powell': 'Powell',
+ 'cg': 'CG',
+ 'bfgs': 'BFGS',
+ 'newton': 'Newton-CG',
+ 'lbfgsb': 'L-BFGS-B',
+ 'l-bfgsb': 'L-BFGS-B',
+ 'tnc': 'TNC',
+ 'cobyla': 'COBYLA',
+ 'slsqp': 'SLSQP',
+ 'dogleg': 'dogleg',
+ 'trust-ncg': 'trust-ncg',
+ 'differential_evolution': 'differential_evolution'}
+
+
+class MinimizerResult(object):
+ """ The result of a minimization.
+
+ Attributes
+ ----------
+ params : Parameters
+ The best-fit parameters
+ success : bool
+ Whether the minimization was successful
+ status : int
+ Termination status of the optimizer. Its value depends on the
+ underlying solver. Refer to `message` for details.
+
+ Notes
+ -----
+ Additional attributes not listed above may be present, depending on the
+ specific solver. Since this class is essentially a subclass of dict
+ with attribute accessors, one can see which attributes are available
+ using the `keys()` method.
+ """
+ def __init__(self, **kws):
+ for key, val in kws.items():
+ setattr(self, key, val)
+
+ @property
+ def flatchain(self):
+ """
+ A flatchain view of the sampling chain from the `emcee` method.
+ """
+ if hasattr(self, 'chain'):
+ if HAS_PANDAS:
+ return pd.DataFrame(self.chain.reshape((-1, self.nvarys)),
+ columns=self.var_names)
+ else:
+ raise NotImplementedError('Please install Pandas to see the '
+ 'flattened chain')
+ else:
+ return None
+
+
+class Minimizer(object):
+ """A general minimizer for curve fitting"""
+ err_nonparam = ("params must be a minimizer.Parameters() instance or list "
+ "of Parameters()")
+ err_maxfev = ("Too many function calls (max set to %i)! Use:"
+ " minimize(func, params, ..., maxfev=NNN)"
+ "or set leastsq_kws['maxfev'] to increase this maximum.")
+
+ def __init__(self, userfcn, params, fcn_args=None, fcn_kws=None,
+ iter_cb=None, scale_covar=True, **kws):
+ """
+ Initialization of the Minimzer class
+
+ Parameters
+ ----------
+ userfcn : callable
+ objective function that returns the residual (difference between
+ model and data) to be minimized in a least squares sense. The
+ function must have the signature:
+ `userfcn(params, *fcn_args, **fcn_kws)`
+ params : lmfit.parameter.Parameters object.
+ contains the Parameters for the model.
+ fcn_args : tuple, optional
+ positional arguments to pass to userfcn.
+ fcn_kws : dict, optional
+ keyword arguments to pass to userfcn.
+ iter_cb : callable, optional
+ Function to be called at each fit iteration. This function should
+ have the signature:
+ `iter_cb(params, iter, resid, *fcn_args, **fcn_kws)`,
+ where where `params` will have the current parameter values, `iter`
+ the iteration, `resid` the current residual array, and `*fcn_args`
+ and `**fcn_kws` as passed to the objective function.
+ scale_covar : bool, optional
+ Whether to automatically scale the covariance matrix (leastsq
+ only).
+ kws : dict, optional
+ Options to pass to the minimizer being used.
+
+ Notes
+ -----
+ The objective function should return the value to be minimized. For the
+ Levenberg-Marquardt algorithm from leastsq(), this returned value must
+ be an array, with a length greater than or equal to the number of
+ fitting variables in the model. For the other methods, the return value
+ can either be a scalar or an array. If an array is returned, the sum of
+ squares of the array will be sent to the underlying fitting method,
+ effectively doing a least-squares optimization of the return values.
+
+ A common use for the fcn_args and fcn_kwds would be to pass in other
+ data needed to calculate the residual, including such things as the
+ data array, dependent variable, uncertainties in the data, and other
+ data structures for the model calculation.
+ """
+ self.userfcn = userfcn
+ self.userargs = fcn_args
+ if self.userargs is None:
+ self.userargs = []
+
+ self.userkws = fcn_kws
+ if self.userkws is None:
+ self.userkws = {}
+ self.kws = kws
+ self.iter_cb = iter_cb
+ self.scale_covar = scale_covar
+ self.nfev = 0
+ self.nfree = 0
+ self.ndata = 0
+ self.ier = 0
+ self._abort = False
+ self.success = True
+ self.errorbars = False
+ self.message = None
+ self.lmdif_message = None
+ self.chisqr = None
+ self.redchi = None
+ self.covar = None
+ self.residual = None
+
+ self.params = params
+ self.jacfcn = None
+
+ @property
+ def values(self):
+ """
+ Returns
+ -------
+ param_values : dict
+ Parameter values in a simple dictionary.
+ """
+
+ return dict([(name, p.value) for name, p in self.result.params.items()])
+
+ def __residual(self, fvars):
+ """
+ Residual function used for least-squares fit.
+ With the new, candidate values of fvars (the fitting variables), this
+ evaluates all parameters, including setting bounds and evaluating
+ constraints, and then passes those to the user-supplied function to
+ calculate the residual.
+ """
+ # set parameter values
+ if self._abort:
+ return None
+ params = self.result.params
+ for name, val in zip(self.result.var_names, fvars):
+ params[name].value = params[name].from_internal(val)
+ self.result.nfev += 1
+
+ params.update_constraints()
+ out = self.userfcn(params, *self.userargs, **self.userkws)
+ if callable(self.iter_cb):
+ abort = self.iter_cb(params, self.result.nfev, out,
+ *self.userargs, **self.userkws)
+ self._abort = self._abort or abort
+ self._abort = self._abort and self.result.nfev > len(fvars)
+ if not self._abort:
+ return np.asarray(out).ravel()
+
+ def __jacobian(self, fvars):
+ """
+ analytical jacobian to be used with the Levenberg-Marquardt
+
+ modified 02-01-2012 by Glenn Jones, Aberystwyth University
+ modified 06-29-2015 M Newville to apply gradient scaling
+ for bounded variables (thanks to JJ Helmus, N Mayorov)
+ """
+ pars = self.result.params
+ grad_scale = ones_like(fvars)
+ for ivar, name in enumerate(self.result.var_names):
+ val = fvars[ivar]
+ pars[name].value = pars[name].from_internal(val)
+ grad_scale[ivar] = pars[name].scale_gradient(val)
+
+ self.result.nfev += 1
+ pars.update_constraints()
+ # compute the jacobian for "internal" unbounded variables,
+ # the rescale for bounded "external" variables.
+ jac = self.jacfcn(pars, *self.userargs, **self.userkws)
+ if self.col_deriv:
+ jac = (jac.transpose()*grad_scale).transpose()
+ else:
+ jac *= grad_scale
+ return jac
+
+ def penalty(self, fvars):
+ """
+ Penalty function for scalar minimizers:
+
+ Parameters
+ ----------
+ fvars : array of values for the variable parameters
+
+ Returns
+ -------
+ r - float
+ The user evaluated user-supplied objective function. If the
+ objective function is an array, return the array sum-of-squares
+ """
+ r = self.__residual(fvars)
+ if isinstance(r, ndarray):
+ r = (r*r).sum()
+ return r
+
+ def prepare_fit(self, params=None):
+ """
+ Prepares parameters for fitting,
+ return array of initial values
+ """
+ # determine which parameters are actually variables
+ # and which are defined expressions.
+ result = self.result = MinimizerResult()
+ if params is not None:
+ self.params = params
+ if isinstance(self.params, Parameters):
+ result.params = deepcopy(self.params)
+ elif isinstance(self.params, (list, tuple)):
+ result.params = Parameters()
+ for par in self.params:
+ if not isinstance(par, Parameter):
+ raise MinimizerException(self.err_nonparam)
+ else:
+ result.params[par.name] = par
+ elif self.params is None:
+ raise MinimizerException(self.err_nonparam)
+
+ # determine which parameters are actually variables
+ # and which are defined expressions.
+
+ result.var_names = [] # note that this *does* belong to self...
+ result.init_vals = []
+ result.params.update_constraints()
+ result.nfev = 0
+ result.errorbars = False
+ result.aborted = False
+ for name, par in self.result.params.items():
+ par.stderr = None
+ par.correl = None
+ if par.expr is not None:
+ par.vary = False
+ if par.vary:
+ result.var_names.append(name)
+ result.init_vals.append(par.setup_bounds())
+
+ par.init_value = par.value
+ if par.name is None:
+ par.name = name
+ result.nvarys = len(result.var_names)
+ return result
+
+ def unprepare_fit(self):
+ """
+ Unprepares the fit, so that subsequent fits will be
+ forced to run prepare_fit.
+
+ removes ast compilations of constraint expressions
+ """
+ pass
+
+ @deprecate(message=' Deprecated in lmfit 0.8.2, use scalar_minimize '
+ 'and method=\'L-BFGS-B\' instead')
+ def lbfgsb(self, **kws):
+ """
+ Use l-bfgs-b minimization
+
+ Parameters
+ ----------
+ kws : dict
+ Minimizer options to pass to the
+ scipy.optimize.lbfgsb.fmin_l_bfgs_b function.
+
+ """
+ raise NotImplementedError("use scalar_minimize(method='L-BFGS-B')")
+
+ @deprecate(message=' Deprecated in lmfit 0.8.2, use scalar_minimize '
+ 'and method=\'Nelder-Mead\' instead')
+ def fmin(self, **kws):
+ """
+ Use Nelder-Mead (simplex) minimization
+
+ Parameters
+ ----------
+ kws : dict
+ Minimizer options to pass to the scipy.optimize.fmin minimizer.
+ """
+ raise NotImplementedError("use scalar_minimize(method='Nelder-Mead')")
+
+ def scalar_minimize(self, method='Nelder-Mead', params=None, **kws):
+ """
+ Use one of the scalar minimization methods from
+ scipy.optimize.minimize.
+
+ Parameters
+ ----------
+ method : str, optional
+ Name of the fitting method to use.
+ One of:
+ 'Nelder-Mead' (default)
+ 'L-BFGS-B'
+ 'Powell'
+ 'CG'
+ 'Newton-CG'
+ 'COBYLA'
+ 'TNC'
+ 'trust-ncg'
+ 'dogleg'
+ 'SLSQP'
+ 'differential_evolution'
+
+ params : Parameters, optional
+ Parameters to use as starting points.
+ kws : dict, optional
+ Minimizer options pass to scipy.optimize.minimize.
+
+ If the objective function returns a numpy array instead
+ of the expected scalar, the sum of squares of the array
+ will be used.
+
+ Note that bounds and constraints can be set on Parameters
+ for any of these methods, so are not supported separately
+ for those designed to use bounds. However, if you use the
+ differential_evolution option you must specify finite
+ (min, max) for each Parameter.
+
+ Returns
+ -------
+ success : bool
+ Whether the fit was successful.
+
+ """
+ if not HAS_SCALAR_MIN:
+ raise NotImplementedError
+
+ result = self.prepare_fit(params=params)
+ vars = result.init_vals
+ params = result.params
+
+ fmin_kws = dict(method=method,
+ options={'maxiter': 1000 * (len(vars) + 1)})
+ fmin_kws.update(self.kws)
+ fmin_kws.update(kws)
+
+ # hess supported only in some methods
+ if 'hess' in fmin_kws and method not in ('Newton-CG',
+ 'dogleg', 'trust-ncg'):
+ fmin_kws.pop('hess')
+
+ # jac supported only in some methods (and Dfun could be used...)
+ if 'jac' not in fmin_kws and fmin_kws.get('Dfun', None) is not None:
+ self.jacfcn = fmin_kws.pop('jac')
+ fmin_kws['jac'] = self.__jacobian
+
+ if 'jac' in fmin_kws and method not in ('CG', 'BFGS', 'Newton-CG',
+ 'dogleg', 'trust-ncg'):
+ self.jacfcn = None
+ fmin_kws.pop('jac')
+
+ if method == 'differential_evolution':
+ fmin_kws['method'] = _differential_evolution
+ bounds = [(par.min, par.max) for par in params.values()]
+ if not np.all(np.isfinite(bounds)):
+ raise ValueError('With differential evolution finite bounds '
+ 'are required for each parameter')
+ bounds = [(-np.pi / 2., np.pi / 2.)] * len(vars)
+ fmin_kws['bounds'] = bounds
+
+ # in scipy 0.14 this can be called directly from scipy_minimize
+ # When minimum scipy is 0.14 the following line and the else
+ # can be removed.
+ ret = _differential_evolution(self.penalty, vars, **fmin_kws)
+ else:
+ ret = scipy_minimize(self.penalty, vars, **fmin_kws)
+
+ result.aborted = self._abort
+ self._abort = False
+ if isinstance(ret, dict):
+ for attr, value in ret.items():
+ setattr(result, attr, value)
+ else:
+ for attr in dir(ret):
+ if not attr.startswith('_'):
+ setattr(result, attr, getattr(ret, attr))
+
+ result.x = np.atleast_1d(result.x)
+ result.chisqr = result.residual = self.__residual(result.x)
+ result.nvarys = len(vars)
+ result.ndata = 1
+ result.nfree = 1
+ if isinstance(result.residual, ndarray):
+ result.chisqr = (result.chisqr**2).sum()
+ result.ndata = len(result.residual)
+ result.nfree = result.ndata - result.nvarys
+ result.redchi = result.chisqr / result.nfree
+ _log_likelihood = result.ndata * np.log(result.redchi)
+ result.aic = _log_likelihood + 2 * result.nvarys
+ result.bic = _log_likelihood + np.log(result.ndata) * result.nvarys
+
+ return result
+
+ def emcee(self, params=None, steps=1000, nwalkers=100, burn=0, thin=1,
+ ntemps=1, pos=None, reuse_sampler=False, workers=1,
+ float_behavior='posterior', is_weighted=True, seed=None):
+ """
+ Bayesian sampling of the posterior distribution for the parameters
+ using the `emcee` Markov Chain Monte Carlo package. The method assumes
+ that the prior is Uniform. You need to have `emcee` installed to use
+ this method.
+
+ Parameters
+ ----------
+ params : lmfit.Parameters, optional
+ Parameters to use as starting point. If this is not specified
+ then the Parameters used to initialise the Minimizer object are
+ used.
+ steps : int, optional
+ How many samples you would like to draw from the posterior
+ distribution for each of the walkers?
+ nwalkers : int, optional
+ Should be set so :math:`nwalkers >> nvarys`, where `nvarys` are
+ the number of parameters being varied during the fit.
+ "Walkers are the members of the ensemble. They are almost like
+ separate Metropolis-Hastings chains but, of course, the proposal
+ distribution for a given walker depends on the positions of all
+ the other walkers in the ensemble." - from the `emcee` webpage.
+ burn : int, optional
+ Discard this many samples from the start of the sampling regime.
+ thin : int, optional
+ Only accept 1 in every `thin` samples.
+ ntemps : int, optional
+ If `ntemps > 1` perform a Parallel Tempering.
+ pos : np.ndarray, optional
+ Specify the initial positions for the sampler. If `ntemps == 1`
+ then `pos.shape` should be `(nwalkers, nvarys)`. Otherwise,
+ `(ntemps, nwalkers, nvarys)`. You can also initialise using a
+ previous chain that had the same `ntemps`, `nwalkers` and
+ `nvarys`. Note that `nvarys` may be one larger than you expect it
+ to be if your `userfcn` returns an array and `is_weighted is
+ False`.
+ reuse_sampler : bool, optional
+ If you have already run `emcee` on a given `Minimizer` object then
+ it possesses an internal ``sampler`` attribute. You can continue to
+ draw from the same sampler (retaining the chain history) if you set
+ this option to `True`. Otherwise a new sampler is created. The
+ `nwalkers`, `ntemps`, `pos`, and `params` keywords are ignored with
+ this option.
+ **Important**: the Parameters used to create the sampler must not
+ change in-between calls to `emcee`. Alteration of Parameters
+ would include changed ``min``, ``max``, ``vary`` and ``expr``
+ attributes. This may happen, for example, if you use an altered
+ Parameters object and call the `minimize` method in-between calls
+ to `emcee`.
+ workers : Pool-like or int, optional
+ For parallelization of sampling. It can be any Pool-like object
+ with a map method that follows the same calling sequence as the
+ built-in `map` function. If int is given as the argument, then a
+ multiprocessing-based pool is spawned internally with the
+ corresponding number of parallel processes. 'mpi4py'-based
+ parallelization and 'joblib'-based parallelization pools can also
+ be used here. **Note**: because of multiprocessing overhead it may
+ only be worth parallelising if the objective function is expensive
+ to calculate, or if there are a large number of objective
+ evaluations per step (`ntemps * nwalkers * nvarys`).
+ float_behavior : str, optional
+ Specifies meaning of the objective function output if it returns a
+ float. One of:
+
+ 'posterior' - objective function returns a log-posterior
+ probability
+ 'chi2' - objective function returns :math:`\chi^2`.
+
+ See Notes for further details.
+ is_weighted : bool, optional
+ Has your objective function been weighted by measurement
+ uncertainties? If `is_weighted is True` then your objective
+ function is assumed to return residuals that have been divided by
+ the true measurement uncertainty `(data - model) / sigma`. If
+ `is_weighted is False` then the objective function is assumed to
+ return unweighted residuals, `data - model`. In this case `emcee`
+ will employ a positive measurement uncertainty during the sampling.
+ This measurement uncertainty will be present in the output params
+ and output chain with the name `__lnsigma`. A side effect of this
+ is that you cannot use this parameter name yourself.
+ **Important** this parameter only has any effect if your objective
+ function returns an array. If your objective function returns a
+ float, then this parameter is ignored. See Notes for more details.
+ seed : int or `np.random.RandomState`, optional
+ If `seed` is an int, a new `np.random.RandomState` instance is used,
+ seeded with `seed`.
+ If `seed` is already a `np.random.RandomState` instance, then that
+ `np.random.RandomState` instance is used.
+ Specify `seed` for repeatable minimizations.
+
+ Returns
+ -------
+ result : MinimizerResult
+ MinimizerResult object containing updated params, statistics,
+ etc. The `MinimizerResult` also contains the ``chain``,
+ ``flatchain`` and ``lnprob`` attributes. The ``chain``
+ and ``flatchain`` attributes contain the samples and have the shape
+ `(nwalkers, (steps - burn) // thin, nvarys)` or
+ `(ntemps, nwalkers, (steps - burn) // thin, nvarys)`,
+ depending on whether Parallel tempering was used or not.
+ `nvarys` is the number of parameters that are allowed to vary.
+ The ``flatchain`` attribute is a `pandas.DataFrame` of the
+ flattened chain, `chain.reshape(-1, nvarys)`. To access flattened
+ chain values for a particular parameter use
+ `result.flatchain[parname]`. The ``lnprob`` attribute contains the
+ log probability for each sample in ``chain``. The sample with the
+ highest probability corresponds to the maximum likelihood estimate.
+
+ Notes
+ -----
+ This method samples the posterior distribution of the parameters using
+ Markov Chain Monte Carlo. To do so it needs to calculate the
+ log-posterior probability of the model parameters, `F`, given the data,
+ `D`, :math:`\ln p(F_{true} | D)`. This 'posterior probability' is
+ calculated as:
+
+ ..math::
+
+ \ln p(F_{true} | D) \propto \ln p(D | F_{true}) + \ln p(F_{true})
+
+ where :math:`\ln p(D | F_{true})` is the 'log-likelihood' and
+ :math:`\ln p(F_{true})` is the 'log-prior'. The default log-prior
+ encodes prior information already known about the model. This method
+ assumes that the log-prior probability is `-np.inf` (impossible) if the
+ one of the parameters is outside its limits. The log-prior probability
+ term is zero if all the parameters are inside their bounds (known as a
+ uniform prior). The log-likelihood function is given by [1]_:
+
+ ..math::
+
+ \ln p(D|F_{true}) = -\frac{1}{2}\sum_n \left[\frac{\left(g_n(F_{true}) - D_n \right)^2}{s_n^2}+\ln (2\pi s_n^2)\right]
+
+ The first summand in the square brackets represents the residual for a
+ given datapoint (:math:`g` being the generative model) . This term
+ represents :math:`\chi^2` when summed over all datapoints.
+ Ideally the objective function used to create `lmfit.Minimizer` should
+ return the log-posterior probability, :math:`\ln p(F_{true} | D)`.
+ However, since the in-built log-prior term is zero, the objective
+ function can also just return the log-likelihood, unless you wish to
+ create a non-uniform prior.
+
+ If a float value is returned by the objective function then this value
+ is assumed by default to be the log-posterior probability, i.e.
+ `float_behavior is 'posterior'`. If your objective function returns
+ :math:`\chi^2`, then you should use a value of `'chi2'` for
+ `float_behavior`. `emcee` will then multiply your :math:`\chi^2` value
+ by -0.5 to obtain the posterior probability.
+
+ However, the default behaviour of many objective functions is to return
+ a vector of (possibly weighted) residuals. Therefore, if your objective
+ function returns a vector, `res`, then the vector is assumed to contain
+ the residuals. If `is_weighted is True` then your residuals are assumed
+ to be correctly weighted by the standard deviation of the data points
+ (`res = (data - model) / sigma`) and the log-likelihood (and
+ log-posterior probability) is calculated as: `-0.5 * np.sum(res **2)`.
+ This ignores the second summand in the square brackets. Consequently,
+ in order to calculate a fully correct log-posterior probability value
+ your objective function should return a single value. If
+ `is_weighted is False` then the data uncertainty, `s_n`, will be
+ treated as a nuisance parameter and will be marginalised out. This is
+ achieved by employing a strictly positive uncertainty
+ (homoscedasticity) for each data point, :math:`s_n = exp(__lnsigma)`.
+ `__lnsigma` will be present in `MinimizerResult.params`, as well as
+ `Minimizer.chain`, `nvarys` will also be increased by one.
+
+ References
+ ----------
+ .. [1] http://dan.iel.fm/emcee/current/user/line/
+ """
+ if not HAS_EMCEE:
+ raise NotImplementedError('You must have emcee to use'
+ ' the emcee method')
+ tparams = params
+ # if you're reusing the sampler then ntemps, nwalkers have to be
+ # determined from the previous sampling
+ if reuse_sampler:
+ if not hasattr(self, 'sampler') or not hasattr(self, '_lastpos'):
+ raise ValueError("You wanted to use an existing sampler, but"
+ "it hasn't been created yet")
+ if len(self._lastpos.shape) == 2:
+ ntemps = 1
+ nwalkers = self._lastpos.shape[0]
+ elif len(self._lastpos.shape) == 3:
+ ntemps = self._lastpos.shape[0]
+ nwalkers = self._lastpos.shape[1]
+ tparams = None
+
+ result = self.prepare_fit(params=tparams)
+ params = result.params
+
+ # check if the userfcn returns a vector of residuals
+ out = self.userfcn(params, *self.userargs, **self.userkws)
+ out = np.asarray(out).ravel()
+ if out.size > 1 and is_weighted is False:
+ # we need to marginalise over a constant data uncertainty
+ if '__lnsigma' not in params:
+ # __lnsigma should already be in params if is_weighted was
+ # previously set to True.
+ params.add('__lnsigma', value=0.01, min=-np.inf, max=np.inf, vary=True)
+ # have to re-prepare the fit
+ result = self.prepare_fit(params)
+ params = result.params
+
+ # Removing internal parameter scaling. We could possibly keep it,
+ # but I don't know how this affects the emcee sampling.
+ bounds = []
+ var_arr = np.zeros(len(result.var_names))
+ i = 0
+ for par in params:
+ param = params[par]
+ if param.expr is not None:
+ param.vary = False
+ if param.vary:
+ var_arr[i] = param.value
+ i += 1
+ else:
+ # don't want to append bounds if they're not being varied.
+ continue
+
+ param.from_internal = lambda val: val
+ lb, ub = param.min, param.max
+ if lb is None or lb is np.nan:
+ lb = -np.inf
+ if ub is None or ub is np.nan:
+ ub = np.inf
+ bounds.append((lb, ub))
+ bounds = np.array(bounds)
+
+ self.nvarys = len(result.var_names)
+
+ # set up multiprocessing options for the samplers
+ auto_pool = None
+ sampler_kwargs = {}
+ if type(workers) is int and workers > 1:
+ auto_pool = multiprocessing.Pool(workers)
+ sampler_kwargs['pool'] = auto_pool
+ elif hasattr(workers, 'map'):
+ sampler_kwargs['pool'] = workers
+
+ # function arguments for the log-probability functions
+ # these values are sent to the log-probability functions by the sampler.
+ lnprob_args = (self.userfcn, params, result.var_names, bounds)
+ lnprob_kwargs = {'is_weighted': is_weighted,
+ 'float_behavior': float_behavior,
+ 'userargs': self.userargs,
+ 'userkws': self.userkws}
+
+ if ntemps > 1:
+ # the prior and likelihood function args and kwargs are the same
+ sampler_kwargs['loglargs'] = lnprob_args
+ sampler_kwargs['loglkwargs'] = lnprob_kwargs
+ sampler_kwargs['logpargs'] = (bounds,)
+ else:
+ sampler_kwargs['args'] = lnprob_args
+ sampler_kwargs['kwargs'] = lnprob_kwargs
+
+ # set up the random number generator
+ rng = _make_random_gen(seed)
+
+ # now initialise the samplers
+ if reuse_sampler:
+ if auto_pool is not None:
+ self.sampler.pool = auto_pool
+
+ p0 = self._lastpos
+ if p0.shape[-1] != self.nvarys:
+ raise ValueError("You cannot reuse the sampler if the number"
+ "of varying parameters has changed")
+ elif ntemps > 1:
+ # Parallel Tempering
+ # jitter the starting position by scaled Gaussian noise
+ p0 = 1 + rng.randn(ntemps, nwalkers, self.nvarys) * 1.e-4
+ p0 *= var_arr
+ self.sampler = emcee.PTSampler(ntemps, nwalkers, self.nvarys,
+ _lnpost, _lnprior, **sampler_kwargs)
+ else:
+ p0 = 1 + rng.randn(nwalkers, self.nvarys) * 1.e-4
+ p0 *= var_arr
+ self.sampler = emcee.EnsembleSampler(nwalkers, self.nvarys,
+ _lnpost, **sampler_kwargs)
+
+ # user supplies an initialisation position for the chain
+ # If you try to run the sampler with p0 of a wrong size then you'll get
+ # a ValueError. Note, you can't initialise with a position if you are
+ # reusing the sampler.
+ if pos is not None and not reuse_sampler:
+ tpos = np.asfarray(pos)
+ if p0.shape == tpos.shape:
+ pass
+ # trying to initialise with a previous chain
+ elif (tpos.shape[0::2] == (nwalkers, self.nvarys)):
+ tpos = tpos[:, -1, :]
+ # initialising with a PTsampler chain.
+ elif ntemps > 1 and tpos.ndim == 4:
+ tpos_shape = list(tpos.shape)
+ tpos_shape.pop(2)
+ if tpos_shape == (ntemps, nwalkers, self.nvarys):
+ tpos = tpos[..., -1, :]
+ else:
+ raise ValueError('pos should have shape (nwalkers, nvarys)'
+ 'or (ntemps, nwalkers, nvarys) if ntemps > 1')
+ p0 = tpos
+
+ # if you specified a seed then you also need to seed the sampler
+ if seed is not None:
+ self.sampler.random_state = rng.get_state()
+
+ # now do a production run, sampling all the time
+ output = self.sampler.run_mcmc(p0, steps)
+ self._lastpos = output[0]
+
+ # discard the burn samples and thin
+ chain = self.sampler.chain[..., burn::thin, :]
+ lnprobability = self.sampler.lnprobability[:, burn::thin]
+
+ flatchain = chain.reshape((-1, self.nvarys))
+
+ quantiles = np.percentile(flatchain, [15.87, 50, 84.13], axis=0)
+
+ for i, var_name in enumerate(result.var_names):
+ std_l, median, std_u = quantiles[:, i]
+ params[var_name].value = median
+ params[var_name].stderr = 0.5 * (std_u - std_l)
+ params[var_name].correl = {}
+
+ params.update_constraints()
+
+ # work out correlation coefficients
+ corrcoefs = np.corrcoef(flatchain.T)
+
+ for i, var_name in enumerate(result.var_names):
+ for j, var_name2 in enumerate(result.var_names):
+ if i != j:
+ result.params[var_name].correl[var_name2] = corrcoefs[i, j]
+
+ result.chain = np.copy(chain)
+ result.lnprob = np.copy(lnprobability)
+ result.errorbars = True
+ result.nvarys = len(result.var_names)
+
+ if auto_pool is not None:
+ auto_pool.terminate()
+
+ return result
+
+ def leastsq(self, params=None, **kws):
+ """
+ Use Levenberg-Marquardt minimization to perform a fit.
+ This assumes that ModelParameters have been stored, and a function to
+ minimize has been properly set up.
+
+ This wraps scipy.optimize.leastsq.
+
+ When possible, this calculates the estimated uncertainties and
+ variable correlations from the covariance matrix.
+
+ Writes outputs to many internal attributes.
+
+ Parameters
+ ----------
+ params : Parameters, optional
+ Parameters to use as starting points.
+ kws : dict, optional
+ Minimizer options to pass to scipy.optimize.leastsq.
+
+ Returns
+ -------
+ success : bool
+ True if fit was successful, False if not.
+ """
+ result = self.prepare_fit(params=params)
+ vars = result.init_vals
+ nvars = len(vars)
+ lskws = dict(full_output=1, xtol=1.e-7, ftol=1.e-7, col_deriv=False,
+ gtol=1.e-7, maxfev=2000*(nvars+1), Dfun=None)
+
+ lskws.update(self.kws)
+ lskws.update(kws)
+
+ self.col_deriv = False
+ if lskws['Dfun'] is not None:
+ self.jacfcn = lskws['Dfun']
+ self.col_deriv = lskws['col_deriv']
+ lskws['Dfun'] = self.__jacobian
+
+ # suppress runtime warnings during fit and error analysis
+ orig_warn_settings = np.geterr()
+ np.seterr(all='ignore')
+
+ lsout = scipy_leastsq(self.__residual, vars, **lskws)
+ _best, _cov, infodict, errmsg, ier = lsout
+ result.aborted = self._abort
+ self._abort = False
+
+ result.residual = resid = infodict['fvec']
+ result.ier = ier
+ result.lmdif_message = errmsg
+ result.message = 'Fit succeeded.'
+ result.success = ier in [1, 2, 3, 4]
+ if result.aborted:
+ result.message = 'Fit aborted by user callback.'
+ result.success = False
+ elif ier == 0:
+ result.message = 'Invalid Input Parameters.'
+ elif ier == 5:
+ result.message = self.err_maxfev % lskws['maxfev']
+ else:
+ result.message = 'Tolerance seems to be too small.'
+
+ result.ndata = len(resid)
+
+ result.chisqr = (resid**2).sum()
+ result.nfree = (result.ndata - nvars)
+ result.redchi = result.chisqr / result.nfree
+ _log_likelihood = result.ndata * np.log(result.redchi)
+ result.aic = _log_likelihood + 2 * nvars
+ result.bic = _log_likelihood + np.log(result.ndata) * nvars
+
+ params = result.params
+
+ # need to map _best values to params, then calculate the
+ # grad for the variable parameters
+ grad = ones_like(_best)
+ vbest = ones_like(_best)
+
+ # ensure that _best, vbest, and grad are not
+ # broken 1-element ndarrays.
+ if len(np.shape(_best)) == 0:
+ _best = np.array([_best])
+ if len(np.shape(vbest)) == 0:
+ vbest = np.array([vbest])
+ if len(np.shape(grad)) == 0:
+ grad = np.array([grad])
+
+ for ivar, name in enumerate(result.var_names):
+ grad[ivar] = params[name].scale_gradient(_best[ivar])
+ vbest[ivar] = params[name].value
+
+ # modified from JJ Helmus' leastsqbound.py
+ infodict['fjac'] = transpose(transpose(infodict['fjac']) /
+ take(grad, infodict['ipvt'] - 1))
+ rvec = dot(triu(transpose(infodict['fjac'])[:nvars, :]),
+ take(eye(nvars), infodict['ipvt'] - 1, 0))
+ try:
+ result.covar = inv(dot(transpose(rvec), rvec))
+ except (LinAlgError, ValueError):
+ result.covar = None
+
+ has_expr = False
+ for par in params.values():
+ par.stderr, par.correl = 0, None
+ has_expr = has_expr or par.expr is not None
+
+ # self.errorbars = error bars were successfully estimated
+ result.errorbars = (result.covar is not None)
+ if result.aborted:
+ result.errorbars = False
+ if result.errorbars:
+ if self.scale_covar:
+ result.covar *= result.redchi
+ for ivar, name in enumerate(result.var_names):
+ par = params[name]
+ par.stderr = sqrt(result.covar[ivar, ivar])
+ par.correl = {}
+ try:
+ result.errorbars = result.errorbars and (par.stderr > 0.0)
+ for jvar, varn2 in enumerate(result.var_names):
+ if jvar != ivar:
+ par.correl[varn2] = (result.covar[ivar, jvar] /
+ (par.stderr * sqrt(result.covar[jvar, jvar])))
+ except:
+ result.errorbars = False
+
+ if has_expr:
+ # uncertainties on constrained parameters:
+ # get values with uncertainties (including correlations),
+ # temporarily set Parameter values to these,
+ # re-evaluate contrained parameters to extract stderr
+ # and then set Parameters back to best-fit value
+ try:
+ uvars = uncertainties.correlated_values(vbest, result.covar)
+ except (LinAlgError, ValueError):
+ uvars = None
+ if uvars is not None:
+ for par in params.values():
+ eval_stderr(par, uvars, result.var_names, params)
+ # restore nominal values
+ for v, nam in zip(uvars, result.var_names):
+ params[nam].value = v.nominal_value
+
+ if not result.errorbars:
+ result.message = '%s. Could not estimate error-bars' % result.message
+
+ np.seterr(**orig_warn_settings)
+ return result
+
+ def minimize(self, method='leastsq', params=None, **kws):
+ """
+ Perform the minimization.
+
+ Parameters
+ ----------
+ method : str, optional
+ Name of the fitting method to use.
+ One of:
+ 'leastsq' - Levenberg-Marquardt (default)
+ 'nelder' - Nelder-Mead
+ 'lbfgsb' - L-BFGS-B
+ 'powell' - Powell
+ 'cg' - Conjugate-Gradient
+ 'newton' - Newton-CG
+ 'cobyla' - Cobyla
+ 'tnc' - Truncate Newton
+ 'trust-ncg' - Trust Newton-CGn
+ 'dogleg' - Dogleg
+ 'slsqp' - Sequential Linear Squares Programming
+ 'differential_evolution' - differential evolution
+
+ params : Parameters, optional
+ parameters to use as starting values
+
+ Returns
+ -------
+ result : MinimizerResult
+
+ MinimizerResult object contains updated params, fit statistics, etc.
+
+ """
+
+ function = self.leastsq
+ kwargs = {'params': params}
+ kwargs.update(kws)
+
+ user_method = method.lower()
+ if user_method.startswith('least'):
+ function = self.leastsq
+ elif HAS_SCALAR_MIN:
+ function = self.scalar_minimize
+ for key, val in SCALAR_METHODS.items():
+ if (key.lower().startswith(user_method) or
+ val.lower().startswith(user_method)):
+ kwargs['method'] = val
+ elif (user_method.startswith('nelder') or
+ user_method.startswith('fmin')):
+ function = self.fmin
+ elif user_method.startswith('lbfgsb'):
+ function = self.lbfgsb
+ return function(**kwargs)
+
+
+def _lnprior(theta, bounds):
+ """
+ Calculates an improper uniform log-prior probability
+
+ Parameters
+ ----------
+ theta : sequence
+ float parameter values (only those being varied)
+ bounds : np.ndarray
+ Lower and upper bounds of parameters that are varying.
+ Has shape (nvarys, 2).
+
+ Returns
+ -------
+ lnprob : float
+ Log prior probability
+ """
+ if (np.any(theta > bounds[:, 1])
+ or np.any(theta < bounds[:, 0])):
+ return -np.inf
+ else:
+ return 0
+
+
+def _lnpost(theta, userfcn, params, var_names, bounds, userargs=(),
+ userkws=None, float_behavior='posterior', is_weighted=True):
+ """
+ Calculates the log-posterior probability. See the `Minimizer.emcee` method
+ for more details
+
+ Parameters
+ ----------
+ theta : sequence
+ float parameter values (only those being varied)
+ userfcn : callable
+ User objective function
+ params : lmfit.Parameters
+ The entire set of Parameters
+ var_names : list
+ The names of the parameters that are varying
+ bounds : np.ndarray
+ Lower and upper bounds of parameters. Has shape (nvarys, 2).
+ userargs : tuple, optional
+ Extra positional arguments required for user objective function
+ userkws : dict, optional
+ Extra keyword arguments required for user objective function
+ float_behavior : str, optional
+ Specifies meaning of objective when it returns a float. One of:
+
+ 'posterior' - objective function returnins a log-posterior
+ probability.
+ 'chi2' - objective function returns a chi2 value.
+
+ is_weighted : bool
+ If `userfcn` returns a vector of residuals then `is_weighted`
+ specifies if the residuals have been weighted by data uncertainties.
+
+ Returns
+ -------
+ lnprob : float
+ Log posterior probability
+ """
+ # the comparison has to be done on theta and bounds. DO NOT inject theta
+ # values into Parameters, then compare Parameters values to the bounds.
+ # Parameters values are clipped to stay within bounds.
+ if (np.any(theta > bounds[:, 1])
+ or np.any(theta < bounds[:, 0])):
+ return -np.inf
+
+ for name, val in zip(var_names, theta):
+ params[name].value = val
+
+ userkwargs = {}
+ if userkws is not None:
+ userkwargs = userkws
+
+ # update the constraints
+ params.update_constraints()
+
+ # now calculate the log-likelihood
+ out = userfcn(params, *userargs, **userkwargs)
+ lnprob = np.asarray(out).ravel()
+
+ if lnprob.size > 1:
+ # objective function returns a vector of residuals
+ if '__lnsigma' in params and not is_weighted:
+ # marginalise over a constant data uncertainty
+ __lnsigma = params['__lnsigma'].value
+ c = np.log(2 * np.pi) + 2 * __lnsigma
+ lnprob = -0.5 * np.sum((lnprob / np.exp(__lnsigma)) ** 2 + c)
+ else:
+ lnprob = -0.5 * (lnprob * lnprob).sum()
+ else:
+ # objective function returns a single value.
+ # use float_behaviour to figure out if the value is posterior or chi2
+ if float_behavior == 'posterior':
+ pass
+ elif float_behavior == 'chi2':
+ lnprob *= -0.5
+ else:
+ raise ValueError("float_behaviour must be either 'posterior' or"
+ " 'chi2' " + float_behavior)
+
+ return lnprob
+
+
+def _make_random_gen(seed):
+ """Turn seed into a np.random.RandomState instance
+
+ If seed is None, return the RandomState singleton used by np.random.
+ If seed is an int, return a new RandomState instance seeded with seed.
+ If seed is already a RandomState instance, return it.
+ Otherwise raise ValueError.
+ """
+ if seed is None or seed is np.random:
+ return np.random.mtrand._rand
+ if isinstance(seed, (numbers.Integral, np.integer)):
+ return np.random.RandomState(seed)
+ if isinstance(seed, np.random.RandomState):
+ return seed
+ raise ValueError('%r cannot be used to seed a numpy.random.RandomState'
+ ' instance' % seed)
+
+
+def minimize(fcn, params, method='leastsq', args=None, kws=None,
+ scale_covar=True, iter_cb=None, **fit_kws):
+ """
+ A general purpose curvefitting function
+ The minimize function takes a objective function to be minimized, a
+ dictionary (lmfit.parameter.Parameters) containing the model parameters,
+ and several optional arguments.
+
+ Parameters
+ ----------
+ fcn : callable
+ objective function that returns the residual (difference between
+ model and data) to be minimized in a least squares sense. The
+ function must have the signature:
+ `fcn(params, *args, **kws)`
+ params : lmfit.parameter.Parameters object.
+ contains the Parameters for the model.
+ method : str, optional
+ Name of the fitting method to use.
+ One of:
+ 'leastsq' - Levenberg-Marquardt (default)
+ 'nelder' - Nelder-Mead
+ 'lbfgsb' - L-BFGS-B
+ 'powell' - Powell
+ 'cg' - Conjugate-Gradient
+ 'newton' - Newton-CG
+ 'cobyla' - Cobyla
+ 'tnc' - Truncate Newton
+ 'trust-ncg' - Trust Newton-CGn
+ 'dogleg' - Dogleg
+ 'slsqp' - Sequential Linear Squares Programming
+ 'differential_evolution' - differential evolution
+
+ args : tuple, optional
+ Positional arguments to pass to fcn.
+ kws : dict, optional
+ keyword arguments to pass to fcn.
+ iter_cb : callable, optional
+ Function to be called at each fit iteration. This function should
+ have the signature `iter_cb(params, iter, resid, *args, **kws)`,
+ where where `params` will have the current parameter values, `iter`
+ the iteration, `resid` the current residual array, and `*args`
+ and `**kws` as passed to the objective function.
+ scale_covar : bool, optional
+ Whether to automatically scale the covariance matrix (leastsq
+ only).
+ fit_kws : dict, optional
+ Options to pass to the minimizer being used.
+
+ Notes
+ -----
+ The objective function should return the value to be minimized. For the
+ Levenberg-Marquardt algorithm from leastsq(), this returned value must
+ be an array, with a length greater than or equal to the number of
+ fitting variables in the model. For the other methods, the return value
+ can either be a scalar or an array. If an array is returned, the sum of
+ squares of the array will be sent to the underlying fitting method,
+ effectively doing a least-squares optimization of the return values.
+
+ A common use for `args` and `kwds` would be to pass in other
+ data needed to calculate the residual, including such things as the
+ data array, dependent variable, uncertainties in the data, and other
+ data structures for the model calculation.
+ """
+ fitter = Minimizer(fcn, params, fcn_args=args, fcn_kws=kws,
+ iter_cb=iter_cb, scale_covar=scale_covar, **fit_kws)
+ return fitter.minimize(method=method)
diff --git a/lmfit/model.py b/lmfit/model.py
index d627c72..5dd1643 100644
--- a/lmfit/model.py
+++ b/lmfit/model.py
@@ -1,1031 +1,1067 @@
-"""
-Concise nonlinear curve fitting.
-"""
-from __future__ import print_function
-import warnings
-import inspect
-import operator
-from copy import deepcopy
-import numpy as np
-from . import Parameters, Parameter, Minimizer
-from .printfuncs import fit_report, ci_report
-from .confidence import conf_interval
-
-from collections import MutableSet
-
-try:
- from collections import OrderedDict
-except ImportError:
- from ordereddict import OrderedDict
-
-# Use pandas.isnull for aligning missing data is pandas is available.
-# otherwise use numpy.isnan
-try:
- from pandas import isnull, Series
-except ImportError:
- isnull = np.isnan
- Series = type(NotImplemented)
-
-def _align(var, mask, data):
- "align missing data, with pandas is available"
- if isinstance(data, Series) and isinstance(var, Series):
- return var.reindex_like(data).dropna()
- elif mask is not None:
- return var[mask]
- return var
-
-
-try:
- from matplotlib import pyplot as plt
- _HAS_MATPLOTLIB = True
-except ImportError:
- _HAS_MATPLOTLIB = False
-
-
-def _ensureMatplotlib(function):
- if _HAS_MATPLOTLIB:
- return function
- else:
- def no_op(*args, **kwargs):
- print('matplotlib module is required for plotting the results')
-
- return no_op
-
-
-class Model(object):
- """Create a model from a user-defined function.
-
- Parameters
- ----------
- func: function to be wrapped
- independent_vars: list of strings or None (default)
- arguments to func that are independent variables
- param_names: list of strings or None (default)
- names of arguments to func that are to be made into parameters
- missing: None, 'none', 'drop', or 'raise'
- 'none' or None: Do not check for null or missing values (default)
- 'drop': Drop null or missing observations in data.
- if pandas is installed, pandas.isnull is used, otherwise
- numpy.isnan is used.
- 'raise': Raise a (more helpful) exception when data contains null
- or missing values.
- name: None or string
- name for the model. When `None` (default) the name is the same as
- the model function (`func`).
-
- Note
- ----
- Parameter names are inferred from the function arguments,
- and a residual function is automatically constructed.
-
- Example
- -------
- >>> def decay(t, tau, N):
- ... return N*np.exp(-t/tau)
- ...
- >>> my_model = Model(decay, independent_vars=['t'])
- """
-
- _forbidden_args = ('data', 'weights', 'params')
- _invalid_ivar = "Invalid independent variable name ('%s') for function %s"
- _invalid_par = "Invalid parameter name ('%s') for function %s"
- _invalid_missing = "missing must be None, 'none', 'drop', or 'raise'."
- _valid_missing = (None, 'none', 'drop', 'raise')
-
- _invalid_hint = "unknown parameter hint '%s' for param '%s'"
- _hint_names = ('value', 'vary', 'min', 'max', 'expr')
-
- def __init__(self, func, independent_vars=None, param_names=None,
- missing='none', prefix='', name=None, **kws):
- self.func = func
- self._prefix = prefix
- self._param_root_names = param_names # will not include prefixes
- self.independent_vars = independent_vars
- self._func_allargs = []
- self._func_haskeywords = False
- if not missing in self._valid_missing:
- raise ValueError(self._invalid_missing)
- self.missing = missing
- self.opts = kws
- self.param_hints = OrderedDict()
- # the following has been changed from OrderedSet for the time being
- self._param_names = []
- self._parse_params()
- if self.independent_vars is None:
- self.independent_vars = []
- if name is None and hasattr(self.func, '__name__'):
- name = self.func.__name__
- self._name = name
-
- def _reprstring(self, long=False):
- out = self._name
- opts = []
- if len(self._prefix) > 0:
- opts.append("prefix='%s'" % (self._prefix))
- if long:
- for k, v in self.opts.items():
- opts.append("%s='%s'" % (k, v))
- if len(opts) > 0:
- out = "%s, %s" % (out, ', '.join(opts))
- return "Model(%s)" % out
-
- @property
- def name(self):
- return self._reprstring(long=False)
-
- @name.setter
- def name(self, value):
- self._name = value
-
- @property
- def prefix(self):
- return self._prefix
-
- @property
- def param_names(self):
- return self._param_names
-
- def __repr__(self):
- return "<lmfit.Model: %s>" % (self.name)
-
- def copy(self, **kwargs):
- """DOES NOT WORK"""
- raise NotImplementedError("Model.copy does not work. Make a new Model")
-
- def _parse_params(self):
- "build params from function arguments"
- if self.func is None:
- return
- argspec = inspect.getargspec(self.func)
- pos_args = argspec.args[:]
- keywords = argspec.keywords
- kw_args = {}
- if argspec.defaults is not None:
- for val in reversed(argspec.defaults):
- kw_args[pos_args.pop()] = val
-
- self._func_haskeywords = keywords is not None
- self._func_allargs = pos_args + list(kw_args.keys())
- allargs = self._func_allargs
-
- if len(allargs) == 0 and keywords is not None:
- return
-
- # default independent_var = 1st argument
- if self.independent_vars is None:
- self.independent_vars = [pos_args[0]]
-
- # default param names: all positional args
- # except independent variables
- self.def_vals = {}
- might_be_param = []
- if self._param_root_names is None:
- self._param_root_names = pos_args[:]
- for key, val in kw_args.items():
- if (not isinstance(val, bool) and
- isinstance(val, (float, int))):
- self._param_root_names.append(key)
- self.def_vals[key] = val
- elif val is None:
- might_be_param.append(key)
- for p in self.independent_vars:
- if p in self._param_root_names:
- self._param_root_names.remove(p)
-
- new_opts = {}
- for opt, val in self.opts.items():
- if (opt in self._param_root_names or opt in might_be_param and
- isinstance(val, Parameter)):
- self.set_param_hint(opt, value=val.value,
- min=val.min, max=val.max, expr=val.expr)
- elif opt in self._func_allargs:
- new_opts[opt] = val
- self.opts = new_opts
-
- names = []
- if self._prefix is None:
- self._prefix = ''
- for pname in self._param_root_names:
- names.append("%s%s" % (self._prefix, pname))
-
- # check variables names for validity
- # The implicit magic in fit() requires us to disallow some
- fname = self.func.__name__
- for arg in self.independent_vars:
- if arg not in allargs or arg in self._forbidden_args:
- raise ValueError(self._invalid_ivar % (arg, fname))
- for arg in names:
- if (self._strip_prefix(arg) not in allargs or
- arg in self._forbidden_args):
- raise ValueError(self._invalid_par % (arg, fname))
- # the following as been changed from OrderedSet for the time being.
- self._param_names = names[:]
-
- def set_param_hint(self, name, **kwargs):
- """set hints for parameter, including optional bounds
- and constraints (value, vary, min, max, expr)
- these will be used by make_params() when building
- default parameters
-
- example:
- model = GaussianModel()
- model.set_param_hint('amplitude', min=-100.0, max=0.)
- """
- npref = len(self._prefix)
- if npref > 0 and name.startswith(self._prefix):
- name = name[npref:]
-
- thishint = {}
- if name in self.param_hints:
- thishint = self.param_hints.pop(name)
- thishint.update(kwargs)
-
- self.param_hints[name] = OrderedDict()
- for key, val in thishint.items():
- if key in self._hint_names:
- self.param_hints[name][key] = val
- else:
- warnings.warn(self._invalid_hint % (key, name))
-
- def make_params(self, verbose=False, **kwargs):
- """create and return a Parameters object for a Model.
- This applies any default values
- """
- params = Parameters()
- # first build parameters defined in param_hints
- # note that composites may define their own additional
- # convenience parameters here
- for basename, hint in self.param_hints.items():
- name = "%s%s" % (self._prefix, basename)
- if name in params:
- par = params[name]
- else:
- par = Parameter(name=name)
- par._delay_asteval = True
- for item in self._hint_names:
- if item in hint:
- setattr(par, item, hint[item])
- # Add the new parameter to self._param_names
- if name not in self._param_names:
- self._param_names.append(name)
- params.add(par)
- if verbose:
- print( ' - Adding parameter for hint "%s"' % name)
-
- # next, make sure that all named parameters are included
- for name in self.param_names:
- if name in params:
- par = params[name]
- else:
- par = Parameter(name=name)
- par._delay_asteval = True
- basename = name[len(self._prefix):]
- # apply defaults from model function definition
- if basename in self.def_vals:
- par.value = self.def_vals[basename]
- # apply defaults from parameter hints
- if basename in self.param_hints:
- hint = self.param_hints[basename]
- for item in self._hint_names:
- if item in hint:
- setattr(par, item, hint[item])
- # apply values passed in through kw args
- if basename in kwargs:
- # kw parameter names with no prefix
- par.value = kwargs[basename]
- if name in kwargs:
- # kw parameter names with prefix
- par.value = kwargs[name]
- params.add(par)
- if verbose:
- print( ' - Adding parameter "%s"' % name)
-
- for p in params.values():
- p._delay_asteval = False
- return params
-
- def guess(self, data=None, **kws):
- """stub for guess starting values --
- should be implemented for each model subclass to
- run self.make_params(), update starting values
- and return a Parameters object"""
- cname = self.__class__.__name__
- msg = 'guess() not implemented for %s' % cname
- raise NotImplementedError(msg)
-
- def _residual(self, params, data, weights, **kwargs):
- "default residual: (data-model)*weights"
- diff = self.eval(params, **kwargs) - data
- if weights is not None:
- diff *= weights
- return np.asarray(diff).ravel() # for compatibility with pandas.Series
-
- def _handle_missing(self, data):
- "handle missing data"
- if self.missing == 'raise':
- if np.any(isnull(data)):
- raise ValueError("Data contains a null value.")
- elif self.missing == 'drop':
- mask = ~isnull(data)
- if np.all(mask):
- return None # short-circuit this -- no missing values
- mask = np.asarray(mask) # for compatibility with pandas.Series
- return mask
-
- def _strip_prefix(self, name):
- npref = len(self._prefix)
- if npref > 0 and name.startswith(self._prefix):
- name = name[npref:]
- return name
-
- def make_funcargs(self, params=None, kwargs=None, strip=True):
- """convert parameter values and keywords to function arguments"""
- if params is None: params = {}
- if kwargs is None: kwargs = {}
- out = {}
- out.update(self.opts)
- for name, par in params.items():
- if strip:
- name = self._strip_prefix(name)
- if name in self._func_allargs or self._func_haskeywords:
- out[name] = par.value
-
- # kwargs handled slightly differently -- may set param value too!
- for name, val in kwargs.items():
- if strip:
- name = self._strip_prefix(name)
- if name in self._func_allargs or self._func_haskeywords:
- out[name] = val
- if name in params:
- params[name].value = val
- return out
-
- def _make_all_args(self, params=None, **kwargs):
- """generate **all** function args for all functions"""
- args = {}
- for key, val in self.make_funcargs(params, kwargs).items():
- args["%s%s" % (self._prefix, key)] = val
- return args
-
- def eval(self, params=None, **kwargs):
- """evaluate the model with the supplied parameters"""
- result = self.func(**self.make_funcargs(params, kwargs))
- # Handle special case of constant result and one
- # independent variable (of any dimension).
- if np.ndim(result) == 0 and len(self.independent_vars) == 1:
- result = np.tile(result, kwargs[self.independent_vars[0]].shape)
- return result
-
- @property
- def components(self):
- """return components for composite model"""
- return [self]
-
- def eval_components(self, params=None, **kwargs):
- """
- evaluate the model with the supplied parameters and returns a ordered
- dict containting name, result pairs.
- """
- key = self._prefix
- if len(key) < 1:
- key = self._name
- return {key: self.eval(params=params, **kwargs)}
-
- def fit(self, data, params=None, weights=None, method='leastsq',
- iter_cb=None, scale_covar=True, verbose=True, fit_kws=None, **kwargs):
- """Fit the model to the data.
-
- Parameters
- ----------
- data: array-like
- params: Parameters object
- weights: array-like of same size as data
- used for weighted fit
- method: fitting method to use (default = 'leastsq')
- iter_cb: None or callable callback function to call at each iteration.
- scale_covar: bool (default True) whether to auto-scale covariance matrix
- verbose: bool (default True) print a message when a new parameter is
- added because of a hint.
- fit_kws: dict
- default fitting options, such as xtol and maxfev, for scipy optimizer
- keyword arguments: optional, named like the arguments of the
- model function, will override params. See examples below.
-
- Returns
- -------
- lmfit.ModelResult
-
- Examples
- --------
- # Take t to be the independent variable and data to be the
- # curve we will fit.
-
- # Using keyword arguments to set initial guesses
- >>> result = my_model.fit(data, tau=5, N=3, t=t)
-
- # Or, for more control, pass a Parameters object.
- >>> result = my_model.fit(data, params, t=t)
-
- # Keyword arguments override Parameters.
- >>> result = my_model.fit(data, params, tau=5, t=t)
-
- Note
- ----
- All parameters, however passed, are copied on input, so the original
- Parameter objects are unchanged.
-
- """
- if params is None:
- params = self.make_params(verbose=verbose)
- else:
- params = deepcopy(params)
-
- # If any kwargs match parameter names, override params.
- param_kwargs = set(kwargs.keys()) & set(self.param_names)
- for name in param_kwargs:
- p = kwargs[name]
- if isinstance(p, Parameter):
- p.name = name # allows N=Parameter(value=5) with implicit name
- params[name] = deepcopy(p)
- else:
- params[name].set(value=p)
- del kwargs[name]
-
- # All remaining kwargs should correspond to independent variables.
- for name in kwargs.keys():
- if name not in self.independent_vars:
- warnings.warn("The keyword argument %s does not" % name +
- "match any arguments of the model function." +
- "It will be ignored.", UserWarning)
-
- # If any parameter is not initialized raise a more helpful error.
- missing_param = any([p not in params.keys()
- for p in self.param_names])
- blank_param = any([(p.value is None and p.expr is None)
- for p in params.values()])
- if missing_param or blank_param:
- msg = ('Assign each parameter an initial value by passing '
- 'Parameters or keyword arguments to fit.\n')
- missing = [p for p in self.param_names if p not in params.keys()]
- blank = [name for name, p in params.items()
- if (p.value is None and p.expr is None)]
- msg += 'Missing parameters: %s\n' % str(missing)
- msg += 'Non initialized parameters: %s' % str(blank)
- raise ValueError(msg)
-
- # Do not alter anything that implements the array interface (np.array, pd.Series)
- # but convert other iterables (e.g., Python lists) to numpy arrays.
- if not hasattr(data, '__array__'):
- data = np.asfarray(data)
- for var in self.independent_vars:
- var_data = kwargs[var]
- if (not hasattr(var_data, '__array__')) and (not np.isscalar(var_data)):
- kwargs[var] = np.asfarray(var_data)
-
- # Handle null/missing values.
- mask = None
- if self.missing not in (None, 'none'):
- mask = self._handle_missing(data) # This can raise.
- if mask is not None:
- data = data[mask]
- if weights is not None:
- weights = _align(weights, mask, data)
-
- # If independent_vars and data are alignable (pandas), align them,
- # and apply the mask from above if there is one.
- for var in self.independent_vars:
- if not np.isscalar(kwargs[var]):
- kwargs[var] = _align(kwargs[var], mask, data)
-
- if fit_kws is None:
- fit_kws = {}
-
- output = ModelResult(self, params, method=method, iter_cb=iter_cb,
- scale_covar=scale_covar, fcn_kws=kwargs,
- **fit_kws)
- output.fit(data=data, weights=weights)
- output.components = self.components
- return output
-
- def __add__(self, other):
- return CompositeModel(self, other, operator.add)
-
- def __sub__(self, other):
- return CompositeModel(self, other, operator.sub)
-
- def __mul__(self, other):
- return CompositeModel(self, other, operator.mul)
-
- def __div__(self, other):
- return CompositeModel(self, other, operator.truediv)
-
- def __truediv__(self, other):
- return CompositeModel(self, other, operator.truediv)
-
-
-class CompositeModel(Model):
- """Create a composite model -- a binary operator of two Models
-
- Parameters
- ----------
- left_model: left-hand side model-- must be a Model()
- right_model: right-hand side model -- must be a Model()
- oper: callable binary operator (typically, operator.add, operator.mul, etc)
-
- independent_vars: list of strings or None (default)
- arguments to func that are independent variables
- param_names: list of strings or None (default)
- names of arguments to func that are to be made into parameters
- missing: None, 'none', 'drop', or 'raise'
- 'none' or None: Do not check for null or missing values (default)
- 'drop': Drop null or missing observations in data.
- if pandas is installed, pandas.isnull is used, otherwise
- numpy.isnan is used.
- 'raise': Raise a (more helpful) exception when data contains null
- or missing values.
- name: None or string
- name for the model. When `None` (default) the name is the same as
- the model function (`func`).
-
- """
- _names_collide = ("\nTwo models have parameters named '{clash}'. "
- "Use distinct names.")
- _bad_arg = "CompositeModel: argument {arg} is not a Model"
- _bad_op = "CompositeModel: operator {op} is not callable"
- _known_ops = {operator.add: '+', operator.sub: '-',
- operator.mul: '*', operator.truediv: '/'}
-
- def __init__(self, left, right, op, **kws):
- if not isinstance(left, Model):
- raise ValueError(self._bad_arg.format(arg=left))
- if not isinstance(right, Model):
- raise ValueError(self._bad_arg.format(arg=right))
- if not callable(op):
- raise ValueError(self._bad_op.format(op=op))
-
- self.left = left
- self.right = right
- self.op = op
-
- name_collisions = set(left.param_names) & set(right.param_names)
- if len(name_collisions) > 0:
- msg = ''
- for collision in name_collisions:
- msg += self._names_collide.format(clash=collision)
- raise NameError(msg)
-
- # we assume that all the sub-models have the same independent vars
- if 'independent_vars' not in kws:
- kws['independent_vars'] = self.left.independent_vars
- if 'missing' not in kws:
- kws['missing'] = self.left.missing
-
- def _tmp(self, *args, **kws): pass
- Model.__init__(self, _tmp, **kws)
-
- for side in (left, right):
- prefix = side.prefix
- for basename, hint in side.param_hints.items():
- self.param_hints["%s%s" % (prefix, basename)] = hint
-
- def _parse_params(self):
- self._func_haskeywords = (self.left._func_haskeywords or
- self.right._func_haskeywords)
- self._func_allargs = (self.left._func_allargs +
- self.right._func_allargs)
- self.def_vals = deepcopy(self.right.def_vals)
- self.def_vals.update(self.left.def_vals)
- self.opts = deepcopy(self.right.opts)
- self.opts.update(self.left.opts)
-
- def _reprstring(self, long=False):
- return "(%s %s %s)" % (self.left._reprstring(long=long),
- self._known_ops.get(self.op, self.op),
- self.right._reprstring(long=long))
-
- def eval(self, params=None, **kwargs):
- return self.op(self.left.eval(params=params, **kwargs),
- self.right.eval(params=params, **kwargs))
-
- def eval_components(self, **kwargs):
- """return ordered dict of name, results for each component"""
- out = OrderedDict(self.left.eval_components(**kwargs))
- out.update(self.right.eval_components(**kwargs))
- return out
-
- @property
- def param_names(self):
- return self.left.param_names + self.right.param_names
-
- @property
- def components(self):
- """return components for composite model"""
- return self.left.components + self.right.components
-
- def _make_all_args(self, params=None, **kwargs):
- """generate **all** function args for all functions"""
- out = self.right._make_all_args(params=params, **kwargs)
- out.update(self.left._make_all_args(params=params, **kwargs))
- return out
-
-
-class ModelResult(Minimizer):
- """Result from Model fit
-
- Attributes
- -----------
- model instance of Model -- the model function
- params instance of Parameters -- the fit parameters
- data array of data values to compare to model
- weights array of weights used in fitting
- init_params copy of params, before being updated by fit()
- init_values array of parameter values, before being updated by fit()
- init_fit model evaluated with init_params.
- best_fit model evaluated with params after being updated by fit()
-
- Methods:
- --------
- fit(data=None, params=None, weights=None, method=None, **kwargs)
- fit (or re-fit) model with params to data (with weights)
- using supplied method. The keyword arguments are sent to
- as keyword arguments to the model function.
-
- all inputs are optional, defaulting to the value used in
- the previous fit. This allows easily changing data or
- parameter settings, or both.
-
- eval(**kwargs)
- evaluate the current model, with the current parameter values,
- with values in kwargs sent to the model function.
-
- eval_components(**kwargs)
- evaluate the current model, with the current parameter values,
- with values in kwargs sent to the model function and returns
- a ordered dict with the model names as the key and the component
- results as the values.
-
- fit_report(modelpars=None, show_correl=True, min_correl=0.1)
- return a fit report.
-
- plot_fit(self, ax=None, datafmt='o', fitfmt='-', initfmt='--',
- numpoints=None, data_kws=None, fit_kws=None, init_kws=None,
- ax_kws=None)
- Plot the fit results using matplotlib.
-
- plot_residuals(self, ax=None, datafmt='o', data_kws=None, fit_kws=None,
- ax_kws=None)
- Plot the fit residuals using matplotlib.
-
- plot(self, datafmt='o', fitfmt='-', initfmt='--', numpoints=None,
- data_kws=None, fit_kws=None, init_kws=None, ax_res_kws=None,
- ax_fit_kws=None, fig_kws=None)
- Plot the fit results and residuals using matplotlib.
- """
- def __init__(self, model, params, data=None, weights=None,
- method='leastsq', fcn_args=None, fcn_kws=None,
- iter_cb=None, scale_covar=True, **fit_kws):
- self.model = model
- self.data = data
- self.weights = weights
- self.method = method
- self.ci_out = None
- self.init_params = deepcopy(params)
- Minimizer.__init__(self, model._residual, params, fcn_args=fcn_args,
- fcn_kws=fcn_kws, iter_cb=iter_cb,
- scale_covar=scale_covar, **fit_kws)
-
- def fit(self, data=None, params=None, weights=None, method=None, **kwargs):
- """perform fit for a Model, given data and params"""
- if data is not None:
- self.data = data
- if params is not None:
- self.init_params = params
- if weights is not None:
- self.weights = weights
- if method is not None:
- self.method = method
- self.ci_out = None
- self.userargs = (self.data, self.weights)
- self.userkws.update(kwargs)
- self.init_fit = self.model.eval(params=self.params, **self.userkws)
-
- _ret = self.minimize(method=self.method)
-
- for attr in dir(_ret):
- if not attr.startswith('_') :
- try:
- setattr(self, attr, getattr(_ret, attr))
- except AttributeError:
- pass
-
- self.init_values = self.model._make_all_args(self.init_params)
- self.best_values = self.model._make_all_args(_ret.params)
- self.best_fit = self.model.eval(params=_ret.params, **self.userkws)
-
- def eval(self, **kwargs):
- self.userkws.update(kwargs)
- return self.model.eval(params=self.params, **self.userkws)
-
- def eval_components(self, **kwargs):
- self.userkws.update(kwargs)
- return self.model.eval_components(params=self.params, **self.userkws)
-
- def conf_interval(self, **kwargs):
- """return explicitly calculated confidence intervals"""
- if self.ci_out is None:
- self.ci_out = conf_interval(self, self, **kwargs)
- return self.ci_out
-
- def ci_report(self, with_offset=True, ndigits=5, **kwargs):
- """return nicely formatted report about confidence intervals"""
- return ci_report(self.conf_interval(**kwargs),
- with_offset=with_offset, ndigits=ndigits)
-
- def fit_report(self, **kwargs):
- "return fit report"
- return '[[Model]]\n %s\n%s\n' % (self.model._reprstring(long=True),
- fit_report(self, **kwargs))
-
- @_ensureMatplotlib
- def plot_fit(self, ax=None, datafmt='o', fitfmt='-', initfmt='--', yerr=None,
- numpoints=None, data_kws=None, fit_kws=None, init_kws=None,
- ax_kws=None):
- """Plot the fit results using matplotlib.
-
- The method will plot results of the fit using matplotlib, including:
- the data points, the initial fit curve and the fitted curve. If the fit
- model included weights, errorbars will also be plotted.
-
- Parameters
- ----------
- ax : matplotlib.axes.Axes, optional
- The axes to plot on. The default in None, which means use the
- current pyplot axis or create one if there is none.
- datafmt : string, optional
- matplotlib format string for data points
- fitfmt : string, optional
- matplotlib format string for fitted curve
- initfmt : string, optional
- matplotlib format string for initial conditions for the fit
- yerr : ndarray, optional
- array of uncertainties for data array
- numpoints : int, optional
- If provided, the final and initial fit curves are evaluated not
- only at data points, but refined to contain `numpoints` points in
- total.
- data_kws : dictionary, optional
- keyword arguments passed on to the plot function for data points
- fit_kws : dictionary, optional
- keyword arguments passed on to the plot function for fitted curve
- init_kws : dictionary, optional
- keyword arguments passed on to the plot function for the initial
- conditions of the fit
- ax_kws : dictionary, optional
- keyword arguments for a new axis, if there is one being created
-
- Returns
- -------
- matplotlib.axes.Axes
-
- Notes
- ----
- For details about plot format strings and keyword arguments see
- documentation of matplotlib.axes.Axes.plot.
-
- If yerr is specified or if the fit model included weights, then
- matplotlib.axes.Axes.errorbar is used to plot the data. If yerr is
- not specified and the fit includes weights, yerr set to 1/self.weights
-
- If `ax` is None then matplotlib.pyplot.gca(**ax_kws) is called.
-
- See Also
- --------
- ModelResult.plot_residuals : Plot the fit residuals using matplotlib.
- ModelResult.plot : Plot the fit results and residuals using matplotlib.
- """
- if data_kws is None:
- data_kws = {}
- if fit_kws is None:
- fit_kws = {}
- if init_kws is None:
- init_kws = {}
- if ax_kws is None:
- ax_kws = {}
-
- if len(self.model.independent_vars) == 1:
- independent_var = self.model.independent_vars[0]
- else:
- print('Fit can only be plotted if the model function has one '
- 'independent variable.')
- return False
-
- if not isinstance(ax, plt.Axes):
- ax = plt.gca(**ax_kws)
-
- x_array = self.userkws[independent_var]
-
- # make a dense array for x-axis if data is not dense
- if numpoints is not None and len(self.data) < numpoints:
- x_array_dense = np.linspace(min(x_array), max(x_array), numpoints)
- else:
- x_array_dense = x_array
-
- ax.plot(x_array_dense, self.model.eval(self.init_params,
- **{independent_var: x_array_dense}), initfmt,
- label='init', **init_kws)
- ax.plot(x_array_dense, self.model.eval(self.params,
- **{independent_var: x_array_dense}), fitfmt,
- label='best-fit', **fit_kws)
-
- if yerr is None and self.weights is not None:
- yerr = 1.0/self.weights
- if yerr is not None:
- ax.errorbar(x_array, self.data, yerr=yerr,
- fmt=datafmt, label='data', **data_kws)
- else:
- ax.plot(x_array, self.data, datafmt, label='data', **data_kws)
-
- ax.set_title(self.model.name)
- ax.set_xlabel(independent_var)
- ax.set_ylabel('y')
- ax.legend()
-
- return ax
-
- @_ensureMatplotlib
- def plot_residuals(self, ax=None, datafmt='o', yerr=None, data_kws=None,
- fit_kws=None, ax_kws=None):
- """Plot the fit residuals using matplotlib.
-
- The method will plot residuals of the fit using matplotlib, including:
- the data points and the fitted curve (as horizontal line). If the fit
- model included weights, errorbars will also be plotted.
-
- Parameters
- ----------
- ax : matplotlib.axes.Axes, optional
- The axes to plot on. The default in None, which means use the
- current pyplot axis or create one if there is none.
- datafmt : string, optional
- matplotlib format string for data points
- yerr : ndarray, optional
- array of uncertainties for data array
- data_kws : dictionary, optional
- keyword arguments passed on to the plot function for data points
- fit_kws : dictionary, optional
- keyword arguments passed on to the plot function for fitted curve
- ax_kws : dictionary, optional
- keyword arguments for a new axis, if there is one being created
-
- Returns
- -------
- matplotlib.axes.Axes
-
- Notes
- ----
- For details about plot format strings and keyword arguments see
- documentation of matplotlib.axes.Axes.plot.
-
- If yerr is specified or if the fit model included weights, then
- matplotlib.axes.Axes.errorbar is used to plot the data. If yerr is
- not specified and the fit includes weights, yerr set to 1/self.weights
-
- If `ax` is None then matplotlib.pyplot.gca(**ax_kws) is called.
-
- See Also
- --------
- ModelResult.plot_fit : Plot the fit results using matplotlib.
- ModelResult.plot : Plot the fit results and residuals using matplotlib.
- """
- if data_kws is None:
- data_kws = {}
- if fit_kws is None:
- fit_kws = {}
- if fit_kws is None:
- fit_kws = {}
- if ax_kws is None:
- ax_kws = {}
-
- if len(self.model.independent_vars) == 1:
- independent_var = self.model.independent_vars[0]
- else:
- print('Fit can only be plotted if the model function has one '
- 'independent variable.')
- return False
-
- if not isinstance(ax, plt.Axes):
- ax = plt.gca(**ax_kws)
-
- x_array = self.userkws[independent_var]
-
- ax.axhline(0, **fit_kws)
-
- if yerr is None and self.weights is not None:
- yerr = 1.0/self.weights
- if yerr is not None:
- ax.errorbar(x_array, self.eval() - self.data, yerr=yerr,
- fmt=datafmt, label='residuals', **data_kws)
- else:
- ax.plot(x_array, self.eval() - self.data, datafmt,
- label='residuals', **data_kws)
-
- ax.set_title(self.model.name)
- ax.set_ylabel('residuals')
- ax.legend()
-
- return ax
-
- @_ensureMatplotlib
- def plot(self, datafmt='o', fitfmt='-', initfmt='--', yerr=None,
- numpoints=None, fig=None, data_kws=None, fit_kws=None,
- init_kws=None, ax_res_kws=None, ax_fit_kws=None,
- fig_kws=None):
- """Plot the fit results and residuals using matplotlib.
-
- The method will produce a matplotlib figure with both results of the
- fit and the residuals plotted. If the fit model included weights,
- errorbars will also be plotted.
-
- Parameters
- ----------
- datafmt : string, optional
- matplotlib format string for data points
- fitfmt : string, optional
- matplotlib format string for fitted curve
- initfmt : string, optional
- matplotlib format string for initial conditions for the fit
- yerr : ndarray, optional
- array of uncertainties for data array
- numpoints : int, optional
- If provided, the final and initial fit curves are evaluated not
- only at data points, but refined to contain `numpoints` points in
- total.
- fig : matplotlib.figure.Figure, optional
- The figure to plot on. The default in None, which means use the
- current pyplot figure or create one if there is none.
- data_kws : dictionary, optional
- keyword arguments passed on to the plot function for data points
- fit_kws : dictionary, optional
- keyword arguments passed on to the plot function for fitted curve
- init_kws : dictionary, optional
- keyword arguments passed on to the plot function for the initial
- conditions of the fit
- ax_res_kws : dictionary, optional
- keyword arguments for the axes for the residuals plot
- ax_fit_kws : dictionary, optional
- keyword arguments for the axes for the fit plot
- fig_kws : dictionary, optional
- keyword arguments for a new figure, if there is one being created
-
- Returns
- -------
- matplotlib.figure.Figure
-
- Notes
- ----
- The method combines ModelResult.plot_fit and ModelResult.plot_residuals.
-
- If yerr is specified or if the fit model included weights, then
- matplotlib.axes.Axes.errorbar is used to plot the data. If yerr is
- not specified and the fit includes weights, yerr set to 1/self.weights
-
- If `fig` is None then matplotlib.pyplot.figure(**fig_kws) is called.
-
- See Also
- --------
- ModelResult.plot_fit : Plot the fit results using matplotlib.
- ModelResult.plot_residuals : Plot the fit residuals using matplotlib.
- """
- if data_kws is None:
- data_kws = {}
- if fit_kws is None:
- fit_kws = {}
- if init_kws is None:
- init_kws = {}
- if ax_res_kws is None:
- ax_res_kws = {}
- if ax_fit_kws is None:
- ax_fit_kws = {}
- if fig_kws is None:
- fig_kws = {}
-
- if len(self.model.independent_vars) != 1:
- print('Fit can only be plotted if the model function has one '
- 'independent variable.')
- return False
-
- if not isinstance(fig, plt.Figure):
- fig = plt.figure(**fig_kws)
-
- gs = plt.GridSpec(nrows=2, ncols=1, height_ratios=[1, 4])
- ax_res = fig.add_subplot(gs[0], **ax_res_kws)
- ax_fit = fig.add_subplot(gs[1], sharex=ax_res, **ax_fit_kws)
-
- self.plot_fit(ax=ax_fit, datafmt=datafmt, fitfmt=fitfmt, yerr=yerr,
- initfmt=initfmt, numpoints=numpoints, data_kws=data_kws,
- fit_kws=fit_kws, init_kws=init_kws, ax_kws=ax_fit_kws)
- self.plot_residuals(ax=ax_res, datafmt=datafmt, yerr=yerr,
- data_kws=data_kws, fit_kws=fit_kws,
- ax_kws=ax_res_kws)
-
- return fig
+"""
+Concise nonlinear curve fitting.
+"""
+from __future__ import print_function
+import warnings
+import inspect
+import operator
+from copy import deepcopy
+import numpy as np
+from . import Parameters, Parameter, Minimizer
+from .printfuncs import fit_report, ci_report
+from .confidence import conf_interval
+
+try:
+ from collections import OrderedDict
+except ImportError:
+ from ordereddict import OrderedDict
+
+# Use pandas.isnull for aligning missing data is pandas is available.
+# otherwise use numpy.isnan
+try:
+ from pandas import isnull, Series
+except ImportError:
+ isnull = np.isnan
+ Series = type(NotImplemented)
+
+def _align(var, mask, data):
+ "align missing data, with pandas is available"
+ if isinstance(data, Series) and isinstance(var, Series):
+ return var.reindex_like(data).dropna()
+ elif mask is not None:
+ return var[mask]
+ return var
+
+
+try:
+ from matplotlib import pyplot as plt
+ _HAS_MATPLOTLIB = True
+except ImportError:
+ _HAS_MATPLOTLIB = False
+
+
+def _ensureMatplotlib(function):
+ if _HAS_MATPLOTLIB:
+ return function
+ else:
+ def no_op(*args, **kwargs):
+ print('matplotlib module is required for plotting the results')
+
+ return no_op
+
+
+class Model(object):
+ """Create a model from a user-defined function.
+
+ Parameters
+ ----------
+ func: function to be wrapped
+ independent_vars: list of strings or None (default)
+ arguments to func that are independent variables
+ param_names: list of strings or None (default)
+ names of arguments to func that are to be made into parameters
+ missing: None, 'none', 'drop', or 'raise'
+ 'none' or None: Do not check for null or missing values (default)
+ 'drop': Drop null or missing observations in data.
+ if pandas is installed, pandas.isnull is used, otherwise
+ numpy.isnan is used.
+ 'raise': Raise a (more helpful) exception when data contains null
+ or missing values.
+ name: None or string
+ name for the model. When `None` (default) the name is the same as
+ the model function (`func`).
+
+ Note
+ ----
+ Parameter names are inferred from the function arguments,
+ and a residual function is automatically constructed.
+
+ Example
+ -------
+ >>> def decay(t, tau, N):
+ ... return N*np.exp(-t/tau)
+ ...
+ >>> my_model = Model(decay, independent_vars=['t'])
+ """
+
+ _forbidden_args = ('data', 'weights', 'params')
+ _invalid_ivar = "Invalid independent variable name ('%s') for function %s"
+ _invalid_par = "Invalid parameter name ('%s') for function %s"
+ _invalid_missing = "missing must be None, 'none', 'drop', or 'raise'."
+ _valid_missing = (None, 'none', 'drop', 'raise')
+
+ _invalid_hint = "unknown parameter hint '%s' for param '%s'"
+ _hint_names = ('value', 'vary', 'min', 'max', 'expr')
+
+ def __init__(self, func, independent_vars=None, param_names=None,
+ missing='none', prefix='', name=None, **kws):
+ self.func = func
+ self._prefix = prefix
+ self._param_root_names = param_names # will not include prefixes
+ self.independent_vars = independent_vars
+ self._func_allargs = []
+ self._func_haskeywords = False
+ if not missing in self._valid_missing:
+ raise ValueError(self._invalid_missing)
+ self.missing = missing
+ self.opts = kws
+ self.param_hints = OrderedDict()
+ # the following has been changed from OrderedSet for the time being
+ self._param_names = []
+ self._parse_params()
+ if self.independent_vars is None:
+ self.independent_vars = []
+ if name is None and hasattr(self.func, '__name__'):
+ name = self.func.__name__
+ self._name = name
+
+ def _reprstring(self, long=False):
+ out = self._name
+ opts = []
+ if len(self._prefix) > 0:
+ opts.append("prefix='%s'" % (self._prefix))
+ if long:
+ for k, v in self.opts.items():
+ opts.append("%s='%s'" % (k, v))
+ if len(opts) > 0:
+ out = "%s, %s" % (out, ', '.join(opts))
+ return "Model(%s)" % out
+
+ @property
+ def name(self):
+ return self._reprstring(long=False)
+
+ @name.setter
+ def name(self, value):
+ self._name = value
+
+ @property
+ def prefix(self):
+ return self._prefix
+
+ @property
+ def param_names(self):
+ return self._param_names
+
+ def __repr__(self):
+ return "<lmfit.Model: %s>" % (self.name)
+
+ def copy(self, **kwargs):
+ """DOES NOT WORK"""
+ raise NotImplementedError("Model.copy does not work. Make a new Model")
+
+ def _parse_params(self):
+ "build params from function arguments"
+ if self.func is None:
+ return
+ argspec = inspect.getargspec(self.func)
+ pos_args = argspec.args[:]
+ keywords = argspec.keywords
+ kw_args = {}
+ if argspec.defaults is not None:
+ for val in reversed(argspec.defaults):
+ kw_args[pos_args.pop()] = val
+
+ self._func_haskeywords = keywords is not None
+ self._func_allargs = pos_args + list(kw_args.keys())
+ allargs = self._func_allargs
+
+ if len(allargs) == 0 and keywords is not None:
+ return
+
+ # default independent_var = 1st argument
+ if self.independent_vars is None:
+ self.independent_vars = [pos_args[0]]
+
+ # default param names: all positional args
+ # except independent variables
+ self.def_vals = {}
+ might_be_param = []
+ if self._param_root_names is None:
+ self._param_root_names = pos_args[:]
+ for key, val in kw_args.items():
+ if (not isinstance(val, bool) and
+ isinstance(val, (float, int))):
+ self._param_root_names.append(key)
+ self.def_vals[key] = val
+ elif val is None:
+ might_be_param.append(key)
+ for p in self.independent_vars:
+ if p in self._param_root_names:
+ self._param_root_names.remove(p)
+
+ new_opts = {}
+ for opt, val in self.opts.items():
+ if (opt in self._param_root_names or opt in might_be_param and
+ isinstance(val, Parameter)):
+ self.set_param_hint(opt, value=val.value,
+ min=val.min, max=val.max, expr=val.expr)
+ elif opt in self._func_allargs:
+ new_opts[opt] = val
+ self.opts = new_opts
+
+ names = []
+ if self._prefix is None:
+ self._prefix = ''
+ for pname in self._param_root_names:
+ names.append("%s%s" % (self._prefix, pname))
+
+ # check variables names for validity
+ # The implicit magic in fit() requires us to disallow some
+ fname = self.func.__name__
+ for arg in self.independent_vars:
+ if arg not in allargs or arg in self._forbidden_args:
+ raise ValueError(self._invalid_ivar % (arg, fname))
+ for arg in names:
+ if (self._strip_prefix(arg) not in allargs or
+ arg in self._forbidden_args):
+ raise ValueError(self._invalid_par % (arg, fname))
+ # the following as been changed from OrderedSet for the time being.
+ self._param_names = names[:]
+
+ def set_param_hint(self, name, **kwargs):
+ """set hints for parameter, including optional bounds
+ and constraints (value, vary, min, max, expr)
+ these will be used by make_params() when building
+ default parameters
+
+ example:
+ model = GaussianModel()
+ model.set_param_hint('amplitude', min=-100.0, max=0.)
+ """
+ npref = len(self._prefix)
+ if npref > 0 and name.startswith(self._prefix):
+ name = name[npref:]
+
+ if name not in self.param_hints:
+ self.param_hints[name] = OrderedDict()
+
+ for key, val in kwargs.items():
+ if key in self._hint_names:
+ self.param_hints[name][key] = val
+ else:
+ warnings.warn(self._invalid_hint % (key, name))
+
+ def print_param_hints(self, colwidth=8):
+ """Prints a nicely aligned text-table of parameters hints.
+
+ The argument `colwidth` is the width of each column,
+ except for first and last columns.
+ """
+ name_len = max(len(s) for s in self.param_hints)
+ print('{:{name_len}} {:>{n}} {:>{n}} {:>{n}} {:>{n}} {:{n}}'
+ .format('Name', 'Value', 'Min', 'Max', 'Vary', 'Expr',
+ name_len=name_len, n=colwidth))
+ line = ('{name:<{name_len}} {value:{n}g} {min:{n}g} {max:{n}g} '
+ '{vary!s:>{n}} {expr}')
+ for name, values in sorted(self.param_hints.items()):
+ pvalues = dict(name=name, value=np.nan, min=-np.inf, max=np.inf,
+ vary=True, expr='')
+ pvalues.update(**values)
+ print(line.format(name_len=name_len, n=colwidth, **pvalues))
+
+ def make_params(self, verbose=False, **kwargs):
+ """create and return a Parameters object for a Model.
+ This applies any default values
+ """
+ params = Parameters()
+
+ # make sure that all named parameters are in params
+ for name in self.param_names:
+ if name in params:
+ par = params[name]
+ else:
+ par = Parameter(name=name)
+ par._delay_asteval = True
+ basename = name[len(self._prefix):]
+ # apply defaults from model function definition
+ if basename in self.def_vals:
+ par.value = self.def_vals[basename]
+ # apply defaults from parameter hints
+ if basename in self.param_hints:
+ hint = self.param_hints[basename]
+ for item in self._hint_names:
+ if item in hint:
+ setattr(par, item, hint[item])
+ # apply values passed in through kw args
+ if basename in kwargs:
+ # kw parameter names with no prefix
+ par.value = kwargs[basename]
+ if name in kwargs:
+ # kw parameter names with prefix
+ par.value = kwargs[name]
+ params.add(par)
+ if verbose:
+ print( ' - Adding parameter "%s"' % name)
+
+ # next build parameters defined in param_hints
+ # note that composites may define their own additional
+ # convenience parameters here
+ for basename, hint in self.param_hints.items():
+ name = "%s%s" % (self._prefix, basename)
+ if name in params:
+ par = params[name]
+ else:
+ par = Parameter(name=name)
+ params.add(par)
+ if verbose:
+ print( ' - Adding parameter for hint "%s"' % name)
+ par._delay_asteval = True
+ for item in self._hint_names:
+ if item in hint:
+ setattr(par, item, hint[item])
+ # Add the new parameter to self._param_names
+ if name not in self._param_names:
+ self._param_names.append(name)
+
+ for p in params.values():
+ p._delay_asteval = False
+ return params
+
+ def guess(self, data=None, **kws):
+ """stub for guess starting values --
+ should be implemented for each model subclass to
+ run self.make_params(), update starting values
+ and return a Parameters object"""
+ cname = self.__class__.__name__
+ msg = 'guess() not implemented for %s' % cname
+ raise NotImplementedError(msg)
+
+ def _residual(self, params, data, weights, **kwargs):
+ """default residual: (data-model)*weights
+
+ If the model returns complex values, the residual is computed by treating the real and imaginary
+ parts separately. In this case, if the weights provided are real, they are assumed to apply equally to the
+ real and imaginary parts. If the weights are complex, the real part of the weights are applied to the real
+ part of the residual and the imaginary part is treated correspondingly.
+
+ Since the underlying scipy.optimize routines expect np.float arrays, the only complex type supported is
+ np.complex.
+
+ The "ravels" throughout are necessary to support pandas.Series.
+ """
+ diff = self.eval(params, **kwargs) - data
+
+ if diff.dtype == np.complex:
+ # data/model are complex
+ diff = diff.ravel().view(np.float)
+ if weights is not None:
+ if weights.dtype == np.complex:
+ # weights are complex
+ weights = weights.ravel().view(np.float)
+ else:
+ # real weights but complex data
+ weights = (weights + 1j * weights).ravel().view(np.float)
+ if weights is not None:
+ diff *= weights
+ return np.asarray(diff).ravel() # for compatibility with pandas.Series
+
+ def _handle_missing(self, data):
+ "handle missing data"
+ if self.missing == 'raise':
+ if np.any(isnull(data)):
+ raise ValueError("Data contains a null value.")
+ elif self.missing == 'drop':
+ mask = ~isnull(data)
+ if np.all(mask):
+ return None # short-circuit this -- no missing values
+ mask = np.asarray(mask) # for compatibility with pandas.Series
+ return mask
+
+ def _strip_prefix(self, name):
+ npref = len(self._prefix)
+ if npref > 0 and name.startswith(self._prefix):
+ name = name[npref:]
+ return name
+
+ def make_funcargs(self, params=None, kwargs=None, strip=True):
+ """convert parameter values and keywords to function arguments"""
+ if params is None: params = {}
+ if kwargs is None: kwargs = {}
+ out = {}
+ out.update(self.opts)
+ for name, par in params.items():
+ if strip:
+ name = self._strip_prefix(name)
+ if name in self._func_allargs or self._func_haskeywords:
+ out[name] = par.value
+
+ # kwargs handled slightly differently -- may set param value too!
+ for name, val in kwargs.items():
+ if strip:
+ name = self._strip_prefix(name)
+ if name in self._func_allargs or self._func_haskeywords:
+ out[name] = val
+ if name in params:
+ params[name].value = val
+ return out
+
+ def _make_all_args(self, params=None, **kwargs):
+ """generate **all** function args for all functions"""
+ args = {}
+ for key, val in self.make_funcargs(params, kwargs).items():
+ args["%s%s" % (self._prefix, key)] = val
+ return args
+
+ def eval(self, params=None, **kwargs):
+ """evaluate the model with the supplied parameters"""
+ result = self.func(**self.make_funcargs(params, kwargs))
+ # Handle special case of constant result and one
+ # independent variable (of any dimension).
+ if np.ndim(result) == 0 and len(self.independent_vars) == 1:
+ result = np.tile(result, kwargs[self.independent_vars[0]].shape)
+ return result
+
+ @property
+ def components(self):
+ """return components for composite model"""
+ return [self]
+
+ def eval_components(self, params=None, **kwargs):
+ """
+ evaluate the model with the supplied parameters and returns a ordered
+ dict containting name, result pairs.
+ """
+ key = self._prefix
+ if len(key) < 1:
+ key = self._name
+ return {key: self.eval(params=params, **kwargs)}
+
+ def fit(self, data, params=None, weights=None, method='leastsq',
+ iter_cb=None, scale_covar=True, verbose=False, fit_kws=None, **kwargs):
+ """Fit the model to the data.
+
+ Parameters
+ ----------
+ data: array-like
+ params: Parameters object
+ weights: array-like of same size as data
+ used for weighted fit
+ method: fitting method to use (default = 'leastsq')
+ iter_cb: None or callable callback function to call at each iteration.
+ scale_covar: bool (default True) whether to auto-scale covariance matrix
+ verbose: bool (default True) print a message when a new parameter is
+ added because of a hint.
+ fit_kws: dict
+ default fitting options, such as xtol and maxfev, for scipy optimizer
+ keyword arguments: optional, named like the arguments of the
+ model function, will override params. See examples below.
+
+ Returns
+ -------
+ lmfit.ModelResult
+
+ Examples
+ --------
+ # Take t to be the independent variable and data to be the
+ # curve we will fit.
+
+ # Using keyword arguments to set initial guesses
+ >>> result = my_model.fit(data, tau=5, N=3, t=t)
+
+ # Or, for more control, pass a Parameters object.
+ >>> result = my_model.fit(data, params, t=t)
+
+ # Keyword arguments override Parameters.
+ >>> result = my_model.fit(data, params, tau=5, t=t)
+
+ Note
+ ----
+ All parameters, however passed, are copied on input, so the original
+ Parameter objects are unchanged.
+
+ """
+ if params is None:
+ params = self.make_params(verbose=verbose)
+ else:
+ params = deepcopy(params)
+
+ # If any kwargs match parameter names, override params.
+ param_kwargs = set(kwargs.keys()) & set(self.param_names)
+ for name in param_kwargs:
+ p = kwargs[name]
+ if isinstance(p, Parameter):
+ p.name = name # allows N=Parameter(value=5) with implicit name
+ params[name] = deepcopy(p)
+ else:
+ params[name].set(value=p)
+ del kwargs[name]
+
+ # All remaining kwargs should correspond to independent variables.
+ for name in kwargs.keys():
+ if name not in self.independent_vars:
+ warnings.warn("The keyword argument %s does not" % name +
+ "match any arguments of the model function." +
+ "It will be ignored.", UserWarning)
+
+ # If any parameter is not initialized raise a more helpful error.
+ missing_param = any([p not in params.keys()
+ for p in self.param_names])
+ blank_param = any([(p.value is None and p.expr is None)
+ for p in params.values()])
+ if missing_param or blank_param:
+ msg = ('Assign each parameter an initial value by passing '
+ 'Parameters or keyword arguments to fit.\n')
+ missing = [p for p in self.param_names if p not in params.keys()]
+ blank = [name for name, p in params.items()
+ if (p.value is None and p.expr is None)]
+ msg += 'Missing parameters: %s\n' % str(missing)
+ msg += 'Non initialized parameters: %s' % str(blank)
+ raise ValueError(msg)
+
+ # Do not alter anything that implements the array interface (np.array, pd.Series)
+ # but convert other iterables (e.g., Python lists) to numpy arrays.
+ if not hasattr(data, '__array__'):
+ data = np.asfarray(data)
+ for var in self.independent_vars:
+ var_data = kwargs[var]
+ if (not hasattr(var_data, '__array__')) and (not np.isscalar(var_data)):
+ kwargs[var] = np.asfarray(var_data)
+
+ # Handle null/missing values.
+ mask = None
+ if self.missing not in (None, 'none'):
+ mask = self._handle_missing(data) # This can raise.
+ if mask is not None:
+ data = data[mask]
+ if weights is not None:
+ weights = _align(weights, mask, data)
+
+ # If independent_vars and data are alignable (pandas), align them,
+ # and apply the mask from above if there is one.
+ for var in self.independent_vars:
+ if not np.isscalar(kwargs[var]):
+ kwargs[var] = _align(kwargs[var], mask, data)
+
+ if fit_kws is None:
+ fit_kws = {}
+
+ output = ModelResult(self, params, method=method, iter_cb=iter_cb,
+ scale_covar=scale_covar, fcn_kws=kwargs,
+ **fit_kws)
+ output.fit(data=data, weights=weights)
+ output.components = self.components
+ return output
+
+ def __add__(self, other):
+ return CompositeModel(self, other, operator.add)
+
+ def __sub__(self, other):
+ return CompositeModel(self, other, operator.sub)
+
+ def __mul__(self, other):
+ return CompositeModel(self, other, operator.mul)
+
+ def __div__(self, other):
+ return CompositeModel(self, other, operator.truediv)
+
+ def __truediv__(self, other):
+ return CompositeModel(self, other, operator.truediv)
+
+
+class CompositeModel(Model):
+ """Create a composite model -- a binary operator of two Models
+
+ Parameters
+ ----------
+ left_model: left-hand side model-- must be a Model()
+ right_model: right-hand side model -- must be a Model()
+ oper: callable binary operator (typically, operator.add, operator.mul, etc)
+
+ independent_vars: list of strings or None (default)
+ arguments to func that are independent variables
+ param_names: list of strings or None (default)
+ names of arguments to func that are to be made into parameters
+ missing: None, 'none', 'drop', or 'raise'
+ 'none' or None: Do not check for null or missing values (default)
+ 'drop': Drop null or missing observations in data.
+ if pandas is installed, pandas.isnull is used, otherwise
+ numpy.isnan is used.
+ 'raise': Raise a (more helpful) exception when data contains null
+ or missing values.
+ name: None or string
+ name for the model. When `None` (default) the name is the same as
+ the model function (`func`).
+
+ """
+ _names_collide = ("\nTwo models have parameters named '{clash}'. "
+ "Use distinct names.")
+ _bad_arg = "CompositeModel: argument {arg} is not a Model"
+ _bad_op = "CompositeModel: operator {op} is not callable"
+ _known_ops = {operator.add: '+', operator.sub: '-',
+ operator.mul: '*', operator.truediv: '/'}
+
+ def __init__(self, left, right, op, **kws):
+ if not isinstance(left, Model):
+ raise ValueError(self._bad_arg.format(arg=left))
+ if not isinstance(right, Model):
+ raise ValueError(self._bad_arg.format(arg=right))
+ if not callable(op):
+ raise ValueError(self._bad_op.format(op=op))
+
+ self.left = left
+ self.right = right
+ self.op = op
+
+ name_collisions = set(left.param_names) & set(right.param_names)
+ if len(name_collisions) > 0:
+ msg = ''
+ for collision in name_collisions:
+ msg += self._names_collide.format(clash=collision)
+ raise NameError(msg)
+
+ # we assume that all the sub-models have the same independent vars
+ if 'independent_vars' not in kws:
+ kws['independent_vars'] = self.left.independent_vars
+ if 'missing' not in kws:
+ kws['missing'] = self.left.missing
+
+ def _tmp(self, *args, **kws): pass
+ Model.__init__(self, _tmp, **kws)
+
+ for side in (left, right):
+ prefix = side.prefix
+ for basename, hint in side.param_hints.items():
+ self.param_hints["%s%s" % (prefix, basename)] = hint
+
+ def _parse_params(self):
+ self._func_haskeywords = (self.left._func_haskeywords or
+ self.right._func_haskeywords)
+ self._func_allargs = (self.left._func_allargs +
+ self.right._func_allargs)
+ self.def_vals = deepcopy(self.right.def_vals)
+ self.def_vals.update(self.left.def_vals)
+ self.opts = deepcopy(self.right.opts)
+ self.opts.update(self.left.opts)
+
+ def _reprstring(self, long=False):
+ return "(%s %s %s)" % (self.left._reprstring(long=long),
+ self._known_ops.get(self.op, self.op),
+ self.right._reprstring(long=long))
+
+ def eval(self, params=None, **kwargs):
+ return self.op(self.left.eval(params=params, **kwargs),
+ self.right.eval(params=params, **kwargs))
+
+ def eval_components(self, **kwargs):
+ """return ordered dict of name, results for each component"""
+ out = OrderedDict(self.left.eval_components(**kwargs))
+ out.update(self.right.eval_components(**kwargs))
+ return out
+
+ @property
+ def param_names(self):
+ return self.left.param_names + self.right.param_names
+
+ @property
+ def components(self):
+ """return components for composite model"""
+ return self.left.components + self.right.components
+
+ def _make_all_args(self, params=None, **kwargs):
+ """generate **all** function args for all functions"""
+ out = self.right._make_all_args(params=params, **kwargs)
+ out.update(self.left._make_all_args(params=params, **kwargs))
+ return out
+
+
+class ModelResult(Minimizer):
+ """Result from Model fit
+
+ Attributes
+ -----------
+ model instance of Model -- the model function
+ params instance of Parameters -- the fit parameters
+ data array of data values to compare to model
+ weights array of weights used in fitting
+ init_params copy of params, before being updated by fit()
+ init_values array of parameter values, before being updated by fit()
+ init_fit model evaluated with init_params.
+ best_fit model evaluated with params after being updated by fit()
+
+ Methods:
+ --------
+ fit(data=None, params=None, weights=None, method=None, **kwargs)
+ fit (or re-fit) model with params to data (with weights)
+ using supplied method. The keyword arguments are sent to
+ as keyword arguments to the model function.
+
+ all inputs are optional, defaulting to the value used in
+ the previous fit. This allows easily changing data or
+ parameter settings, or both.
+
+ eval(**kwargs)
+ evaluate the current model, with the current parameter values,
+ with values in kwargs sent to the model function.
+
+ eval_components(**kwargs)
+ evaluate the current model, with the current parameter values,
+ with values in kwargs sent to the model function and returns
+ a ordered dict with the model names as the key and the component
+ results as the values.
+
+ fit_report(modelpars=None, show_correl=True, min_correl=0.1)
+ return a fit report.
+
+ plot_fit(self, ax=None, datafmt='o', fitfmt='-', initfmt='--',
+ numpoints=None, data_kws=None, fit_kws=None, init_kws=None,
+ ax_kws=None)
+ Plot the fit results using matplotlib.
+
+ plot_residuals(self, ax=None, datafmt='o', data_kws=None, fit_kws=None,
+ ax_kws=None)
+ Plot the fit residuals using matplotlib.
+
+ plot(self, datafmt='o', fitfmt='-', initfmt='--', numpoints=None,
+ data_kws=None, fit_kws=None, init_kws=None, ax_res_kws=None,
+ ax_fit_kws=None, fig_kws=None)
+ Plot the fit results and residuals using matplotlib.
+ """
+ def __init__(self, model, params, data=None, weights=None,
+ method='leastsq', fcn_args=None, fcn_kws=None,
+ iter_cb=None, scale_covar=True, **fit_kws):
+ self.model = model
+ self.data = data
+ self.weights = weights
+ self.method = method
+ self.ci_out = None
+ self.init_params = deepcopy(params)
+ Minimizer.__init__(self, model._residual, params, fcn_args=fcn_args,
+ fcn_kws=fcn_kws, iter_cb=iter_cb,
+ scale_covar=scale_covar, **fit_kws)
+
+ def fit(self, data=None, params=None, weights=None, method=None, **kwargs):
+ """perform fit for a Model, given data and params"""
+ if data is not None:
+ self.data = data
+ if params is not None:
+ self.init_params = params
+ if weights is not None:
+ self.weights = weights
+ if method is not None:
+ self.method = method
+ self.ci_out = None
+ self.userargs = (self.data, self.weights)
+ self.userkws.update(kwargs)
+ self.init_fit = self.model.eval(params=self.params, **self.userkws)
+
+ _ret = self.minimize(method=self.method)
+
+ for attr in dir(_ret):
+ if not attr.startswith('_') :
+ try:
+ setattr(self, attr, getattr(_ret, attr))
+ except AttributeError:
+ pass
+
+ self.init_values = self.model._make_all_args(self.init_params)
+ self.best_values = self.model._make_all_args(_ret.params)
+ self.best_fit = self.model.eval(params=_ret.params, **self.userkws)
+
+ def eval(self, **kwargs):
+ self.userkws.update(kwargs)
+ return self.model.eval(params=self.params, **self.userkws)
+
+ def eval_components(self, **kwargs):
+ self.userkws.update(kwargs)
+ return self.model.eval_components(params=self.params, **self.userkws)
+
+ def conf_interval(self, **kwargs):
+ """return explicitly calculated confidence intervals"""
+ if self.ci_out is None:
+ self.ci_out = conf_interval(self, self, **kwargs)
+ return self.ci_out
+
+ def ci_report(self, with_offset=True, ndigits=5, **kwargs):
+ """return nicely formatted report about confidence intervals"""
+ return ci_report(self.conf_interval(**kwargs),
+ with_offset=with_offset, ndigits=ndigits)
+
+ def fit_report(self, **kwargs):
+ "return fit report"
+ return '[[Model]]\n %s\n%s\n' % (self.model._reprstring(long=True),
+ fit_report(self, **kwargs))
+
+ @_ensureMatplotlib
+ def plot_fit(self, ax=None, datafmt='o', fitfmt='-', initfmt='--', yerr=None,
+ numpoints=None, data_kws=None, fit_kws=None, init_kws=None,
+ ax_kws=None):
+ """Plot the fit results using matplotlib.
+
+ The method will plot results of the fit using matplotlib, including:
+ the data points, the initial fit curve and the fitted curve. If the fit
+ model included weights, errorbars will also be plotted.
+
+ Parameters
+ ----------
+ ax : matplotlib.axes.Axes, optional
+ The axes to plot on. The default in None, which means use the
+ current pyplot axis or create one if there is none.
+ datafmt : string, optional
+ matplotlib format string for data points
+ fitfmt : string, optional
+ matplotlib format string for fitted curve
+ initfmt : string, optional
+ matplotlib format string for initial conditions for the fit
+ yerr : ndarray, optional
+ array of uncertainties for data array
+ numpoints : int, optional
+ If provided, the final and initial fit curves are evaluated not
+ only at data points, but refined to contain `numpoints` points in
+ total.
+ data_kws : dictionary, optional
+ keyword arguments passed on to the plot function for data points
+ fit_kws : dictionary, optional
+ keyword arguments passed on to the plot function for fitted curve
+ init_kws : dictionary, optional
+ keyword arguments passed on to the plot function for the initial
+ conditions of the fit
+ ax_kws : dictionary, optional
+ keyword arguments for a new axis, if there is one being created
+
+ Returns
+ -------
+ matplotlib.axes.Axes
+
+ Notes
+ ----
+ For details about plot format strings and keyword arguments see
+ documentation of matplotlib.axes.Axes.plot.
+
+ If yerr is specified or if the fit model included weights, then
+ matplotlib.axes.Axes.errorbar is used to plot the data. If yerr is
+ not specified and the fit includes weights, yerr set to 1/self.weights
+
+ If `ax` is None then matplotlib.pyplot.gca(**ax_kws) is called.
+
+ See Also
+ --------
+ ModelResult.plot_residuals : Plot the fit residuals using matplotlib.
+ ModelResult.plot : Plot the fit results and residuals using matplotlib.
+ """
+ if data_kws is None:
+ data_kws = {}
+ if fit_kws is None:
+ fit_kws = {}
+ if init_kws is None:
+ init_kws = {}
+ if ax_kws is None:
+ ax_kws = {}
+
+ if len(self.model.independent_vars) == 1:
+ independent_var = self.model.independent_vars[0]
+ else:
+ print('Fit can only be plotted if the model function has one '
+ 'independent variable.')
+ return False
+
+ if not isinstance(ax, plt.Axes):
+ ax = plt.gca(**ax_kws)
+
+ x_array = self.userkws[independent_var]
+
+ # make a dense array for x-axis if data is not dense
+ if numpoints is not None and len(self.data) < numpoints:
+ x_array_dense = np.linspace(min(x_array), max(x_array), numpoints)
+ else:
+ x_array_dense = x_array
+
+ ax.plot(x_array_dense, self.model.eval(self.init_params,
+ **{independent_var: x_array_dense}), initfmt,
+ label='init', **init_kws)
+ ax.plot(x_array_dense, self.model.eval(self.params,
+ **{independent_var: x_array_dense}), fitfmt,
+ label='best-fit', **fit_kws)
+
+ if yerr is None and self.weights is not None:
+ yerr = 1.0/self.weights
+ if yerr is not None:
+ ax.errorbar(x_array, self.data, yerr=yerr,
+ fmt=datafmt, label='data', **data_kws)
+ else:
+ ax.plot(x_array, self.data, datafmt, label='data', **data_kws)
+
+ ax.set_title(self.model.name)
+ ax.set_xlabel(independent_var)
+ ax.set_ylabel('y')
+ ax.legend()
+
+ return ax
+
+ @_ensureMatplotlib
+ def plot_residuals(self, ax=None, datafmt='o', yerr=None, data_kws=None,
+ fit_kws=None, ax_kws=None):
+ """Plot the fit residuals using matplotlib.
+
+ The method will plot residuals of the fit using matplotlib, including:
+ the data points and the fitted curve (as horizontal line). If the fit
+ model included weights, errorbars will also be plotted.
+
+ Parameters
+ ----------
+ ax : matplotlib.axes.Axes, optional
+ The axes to plot on. The default in None, which means use the
+ current pyplot axis or create one if there is none.
+ datafmt : string, optional
+ matplotlib format string for data points
+ yerr : ndarray, optional
+ array of uncertainties for data array
+ data_kws : dictionary, optional
+ keyword arguments passed on to the plot function for data points
+ fit_kws : dictionary, optional
+ keyword arguments passed on to the plot function for fitted curve
+ ax_kws : dictionary, optional
+ keyword arguments for a new axis, if there is one being created
+
+ Returns
+ -------
+ matplotlib.axes.Axes
+
+ Notes
+ ----
+ For details about plot format strings and keyword arguments see
+ documentation of matplotlib.axes.Axes.plot.
+
+ If yerr is specified or if the fit model included weights, then
+ matplotlib.axes.Axes.errorbar is used to plot the data. If yerr is
+ not specified and the fit includes weights, yerr set to 1/self.weights
+
+ If `ax` is None then matplotlib.pyplot.gca(**ax_kws) is called.
+
+ See Also
+ --------
+ ModelResult.plot_fit : Plot the fit results using matplotlib.
+ ModelResult.plot : Plot the fit results and residuals using matplotlib.
+ """
+ if data_kws is None:
+ data_kws = {}
+ if fit_kws is None:
+ fit_kws = {}
+ if fit_kws is None:
+ fit_kws = {}
+ if ax_kws is None:
+ ax_kws = {}
+
+ if len(self.model.independent_vars) == 1:
+ independent_var = self.model.independent_vars[0]
+ else:
+ print('Fit can only be plotted if the model function has one '
+ 'independent variable.')
+ return False
+
+ if not isinstance(ax, plt.Axes):
+ ax = plt.gca(**ax_kws)
+
+ x_array = self.userkws[independent_var]
+
+ ax.axhline(0, **fit_kws)
+
+ if yerr is None and self.weights is not None:
+ yerr = 1.0/self.weights
+ if yerr is not None:
+ ax.errorbar(x_array, self.eval() - self.data, yerr=yerr,
+ fmt=datafmt, label='residuals', **data_kws)
+ else:
+ ax.plot(x_array, self.eval() - self.data, datafmt,
+ label='residuals', **data_kws)
+
+ ax.set_title(self.model.name)
+ ax.set_ylabel('residuals')
+ ax.legend()
+
+ return ax
+
+ @_ensureMatplotlib
+ def plot(self, datafmt='o', fitfmt='-', initfmt='--', yerr=None,
+ numpoints=None, fig=None, data_kws=None, fit_kws=None,
+ init_kws=None, ax_res_kws=None, ax_fit_kws=None,
+ fig_kws=None):
+ """Plot the fit results and residuals using matplotlib.
+
+ The method will produce a matplotlib figure with both results of the
+ fit and the residuals plotted. If the fit model included weights,
+ errorbars will also be plotted.
+
+ Parameters
+ ----------
+ datafmt : string, optional
+ matplotlib format string for data points
+ fitfmt : string, optional
+ matplotlib format string for fitted curve
+ initfmt : string, optional
+ matplotlib format string for initial conditions for the fit
+ yerr : ndarray, optional
+ array of uncertainties for data array
+ numpoints : int, optional
+ If provided, the final and initial fit curves are evaluated not
+ only at data points, but refined to contain `numpoints` points in
+ total.
+ fig : matplotlib.figure.Figure, optional
+ The figure to plot on. The default in None, which means use the
+ current pyplot figure or create one if there is none.
+ data_kws : dictionary, optional
+ keyword arguments passed on to the plot function for data points
+ fit_kws : dictionary, optional
+ keyword arguments passed on to the plot function for fitted curve
+ init_kws : dictionary, optional
+ keyword arguments passed on to the plot function for the initial
+ conditions of the fit
+ ax_res_kws : dictionary, optional
+ keyword arguments for the axes for the residuals plot
+ ax_fit_kws : dictionary, optional
+ keyword arguments for the axes for the fit plot
+ fig_kws : dictionary, optional
+ keyword arguments for a new figure, if there is one being created
+
+ Returns
+ -------
+ matplotlib.figure.Figure
+
+ Notes
+ ----
+ The method combines ModelResult.plot_fit and ModelResult.plot_residuals.
+
+ If yerr is specified or if the fit model included weights, then
+ matplotlib.axes.Axes.errorbar is used to plot the data. If yerr is
+ not specified and the fit includes weights, yerr set to 1/self.weights
+
+ If `fig` is None then matplotlib.pyplot.figure(**fig_kws) is called.
+
+ See Also
+ --------
+ ModelResult.plot_fit : Plot the fit results using matplotlib.
+ ModelResult.plot_residuals : Plot the fit residuals using matplotlib.
+ """
+ if data_kws is None:
+ data_kws = {}
+ if fit_kws is None:
+ fit_kws = {}
+ if init_kws is None:
+ init_kws = {}
+ if ax_res_kws is None:
+ ax_res_kws = {}
+ if ax_fit_kws is None:
+ ax_fit_kws = {}
+ if fig_kws is None:
+ fig_kws = {}
+
+ if len(self.model.independent_vars) != 1:
+ print('Fit can only be plotted if the model function has one '
+ 'independent variable.')
+ return False
+
+ if not isinstance(fig, plt.Figure):
+ fig = plt.figure(**fig_kws)
+
+ gs = plt.GridSpec(nrows=2, ncols=1, height_ratios=[1, 4])
+ ax_res = fig.add_subplot(gs[0], **ax_res_kws)
+ ax_fit = fig.add_subplot(gs[1], sharex=ax_res, **ax_fit_kws)
+
+ self.plot_fit(ax=ax_fit, datafmt=datafmt, fitfmt=fitfmt, yerr=yerr,
+ initfmt=initfmt, numpoints=numpoints, data_kws=data_kws,
+ fit_kws=fit_kws, init_kws=init_kws, ax_kws=ax_fit_kws)
+ self.plot_residuals(ax=ax_res, datafmt=datafmt, yerr=yerr,
+ data_kws=data_kws, fit_kws=fit_kws,
+ ax_kws=ax_res_kws)
+
+ return fig
diff --git a/lmfit/models.py b/lmfit/models.py
index 87139b0..78d024d 100644
--- a/lmfit/models.py
+++ b/lmfit/models.py
@@ -1,454 +1,484 @@
-import numpy as np
-from .model import Model
-
-from .lineshapes import (gaussian, lorentzian, voigt, pvoigt, moffat, pearson7,
- step, rectangle, breit_wigner, logistic,
- students_t, lognormal, damped_oscillator,
- expgaussian, skewed_gaussian, donaich,
- skewed_voigt, exponential, powerlaw, linear,
- parabolic)
-
-from . import lineshapes
-
-from .asteval import Interpreter
-from .astutils import get_ast_names
-
-class DimensionalError(Exception):
- pass
-
-def _validate_1d(independent_vars):
- if len(independent_vars) != 1:
- raise DimensionalError(
- "This model requires exactly one independent variable.")
-
-def index_of(arr, val):
- """return index of array nearest to a value
- """
- if val < min(arr):
- return 0
- return np.abs(arr-val).argmin()
-
-def fwhm_expr(model):
- "return constraint expression for fwhm"
- return "%.7f*%ssigma" % (model.fwhm_factor, model.prefix)
-
-def guess_from_peak(model, y, x, negative, ampscale=1.0, sigscale=1.0):
- "estimate amp, cen, sigma for a peak, create params"
- if x is None:
- return 1.0, 0.0, 1.0
- maxy, miny = max(y), min(y)
- maxx, minx = max(x), min(x)
- imaxy = index_of(y, maxy)
- cen = x[imaxy]
- amp = (maxy - miny)*2.0
- sig = (maxx-minx)/6.0
-
- halfmax_vals = np.where(y > (maxy+miny)/2.0)[0]
- if negative:
- imaxy = index_of(y, miny)
- amp = -(maxy - miny)*2.0
- halfmax_vals = np.where(y < (maxy+miny)/2.0)[0]
- if len(halfmax_vals) > 2:
- sig = (x[halfmax_vals[-1]] - x[halfmax_vals[0]])/2.0
- cen = x[halfmax_vals].mean()
- amp = amp*sig*ampscale
- sig = sig*sigscale
-
- pars = model.make_params(amplitude=amp, center=cen, sigma=sig)
- pars['%ssigma' % model.prefix].set(min=0.0)
- return pars
-
-def update_param_vals(pars, prefix, **kwargs):
- """convenience function to update parameter values
- with keyword arguments"""
- for key, val in kwargs.items():
- pname = "%s%s" % (prefix, key)
- if pname in pars:
- pars[pname].value = val
- return pars
-
-COMMON_DOC = """
-
-Parameters
-----------
-independent_vars: list of strings to be set as variable names
-missing: None, 'drop', or 'raise'
- None: Do not check for null or missing values.
- 'drop': Drop null or missing observations in data.
- Use pandas.isnull if pandas is available; otherwise,
- silently fall back to numpy.isnan.
- 'raise': Raise a (more helpful) exception when data contains null
- or missing values.
-prefix: string to prepend to paramter names, needed to add two Models that
- have parameter names in common. None by default.
-"""
-
-class ConstantModel(Model):
- __doc__ = "x -> c" + COMMON_DOC
- def __init__(self, *args, **kwargs):
- def constant(x, c):
- return c
- super(ConstantModel, self).__init__(constant, *args, **kwargs)
-
- def guess(self, data, **kwargs):
- pars = self.make_params()
- pars['%sc' % self.prefix].set(value=data.mean())
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class LinearModel(Model):
- __doc__ = linear.__doc__ + COMMON_DOC if linear.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(LinearModel, self).__init__(linear, *args, **kwargs)
-
- def guess(self, data, x=None, **kwargs):
- sval, oval = 0., 0.
- if x is not None:
- sval, oval = np.polyfit(x, data, 1)
- pars = self.make_params(intercept=oval, slope=sval)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class QuadraticModel(Model):
- __doc__ = parabolic.__doc__ + COMMON_DOC if parabolic.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(QuadraticModel, self).__init__(parabolic, *args, **kwargs)
-
- def guess(self, data, x=None, **kwargs):
- a, b, c = 0., 0., 0.
- if x is not None:
- a, b, c = np.polyfit(x, data, 2)
- pars = self.make_params(a=a, b=b, c=c)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-ParabolicModel = QuadraticModel
-
-class PolynomialModel(Model):
- __doc__ = "x -> c0 + c1 * x + c2 * x**2 + ... c7 * x**7" + COMMON_DOC
- MAX_DEGREE=7
- DEGREE_ERR = "degree must be an integer less than %d."
- def __init__(self, degree, *args, **kwargs):
- if not isinstance(degree, int) or degree > self.MAX_DEGREE:
- raise TypeError(self.DEGREE_ERR % self.MAX_DEGREE)
-
- self.poly_degree = degree
- pnames = ['c%i' % (i) for i in range(degree + 1)]
- kwargs['param_names'] = pnames
-
- def polynomial(x, c0=0, c1=0, c2=0, c3=0, c4=0, c5=0, c6=0, c7=0):
- return np.polyval([c7, c6, c5, c4, c3, c2, c1, c0], x)
-
- super(PolynomialModel, self).__init__(polynomial, *args, **kwargs)
-
- def guess(self, data, x=None, **kwargs):
- pars = self.make_params()
- if x is not None:
- out = np.polyfit(x, data, self.poly_degree)
- for i, coef in enumerate(out[::-1]):
- pars['%sc%i'% (self.prefix, i)].set(value=coef)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class GaussianModel(Model):
- __doc__ = gaussian.__doc__ + COMMON_DOC if gaussian.__doc__ else ""
- fwhm_factor = 2.354820
- def __init__(self, *args, **kwargs):
- super(GaussianModel, self).__init__(gaussian, *args, **kwargs)
- self.set_param_hint('sigma', min=0)
- self.set_param_hint('fwhm', expr=fwhm_expr(self))
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class LorentzianModel(Model):
- __doc__ = lorentzian.__doc__ + COMMON_DOC if lorentzian.__doc__ else ""
- fwhm_factor = 2.0
- def __init__(self, *args, **kwargs):
- super(LorentzianModel, self).__init__(lorentzian, *args, **kwargs)
- self.set_param_hint('sigma', min=0)
- self.set_param_hint('fwhm', expr=fwhm_expr(self))
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative, ampscale=1.25)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class VoigtModel(Model):
- __doc__ = voigt.__doc__ + COMMON_DOC if voigt.__doc__ else ""
- fwhm_factor = 3.60131
- def __init__(self, *args, **kwargs):
- super(VoigtModel, self).__init__(voigt, *args, **kwargs)
- self.set_param_hint('sigma', min=0)
- self.set_param_hint('gamma', expr='%ssigma' % self.prefix)
- self.set_param_hint('fwhm', expr=fwhm_expr(self))
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative,
- ampscale=1.5, sigscale=0.65)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class PseudoVoigtModel(Model):
- __doc__ = pvoigt.__doc__ + COMMON_DOC if pvoigt.__doc__ else ""
- fwhm_factor = 2.0
- def __init__(self, *args, **kwargs):
- super(PseudoVoigtModel, self).__init__(pvoigt, *args, **kwargs)
- self.set_param_hint('fraction', value=0.5)
- self.set_param_hint('fwhm', expr=fwhm_expr(self))
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative, ampscale=1.25)
- pars['%sfraction' % self.prefix].set(value=0.5)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class MoffatModel(Model):
- __doc__ = moffat.__doc__ + COMMON_DOC if moffat.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(MoffatModel, self).__init__(moffat, *args, **kwargs)
- self.set_param_hint('fwhm', expr="2*%ssigma*sqrt(2**(1.0/%sbeta)-1)" % (self.prefix, self.prefix))
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative, ampscale=0.5, sigscale=1.)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class Pearson7Model(Model):
- __doc__ = pearson7.__doc__ + COMMON_DOC if pearson7.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(Pearson7Model, self).__init__(pearson7, *args, **kwargs)
- self.set_param_hint('expon', value=1.5)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative)
- pars['%sexpon' % self.prefix].set(value=1.5)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class StudentsTModel(Model):
- __doc__ = students_t.__doc__ + COMMON_DOC if students_t.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(StudentsTModel, self).__init__(students_t, *args, **kwargs)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class BreitWignerModel(Model):
- __doc__ = breit_wigner.__doc__ + COMMON_DOC if breit_wigner.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(BreitWignerModel, self).__init__(breit_wigner, *args, **kwargs)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative)
- pars['%sq' % self.prefix].set(value=1.0)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class LognormalModel(Model):
- __doc__ = lognormal.__doc__ + COMMON_DOC if lognormal.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(LognormalModel, self).__init__(lognormal, *args, **kwargs)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = self.make_params(amplitude=1.0, center=0.0, sigma=0.25)
- pars['%ssigma' % self.prefix].set(min=0.0)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class DampedOscillatorModel(Model):
- __doc__ = damped_oscillator.__doc__ + COMMON_DOC if damped_oscillator.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(DampedOscillatorModel, self).__init__(damped_oscillator, *args, **kwargs)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars =guess_from_peak(self, data, x, negative,
- ampscale=0.1, sigscale=0.1)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-class ExponentialGaussianModel(Model):
- __doc__ = expgaussian.__doc__ + COMMON_DOC if expgaussian.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(ExponentialGaussianModel, self).__init__(expgaussian, *args, **kwargs)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-class SkewedGaussianModel(Model):
- __doc__ = skewed_gaussian.__doc__ + COMMON_DOC if skewed_gaussian.__doc__ else ""
- fwhm_factor = 2.354820
- def __init__(self, *args, **kwargs):
- super(SkewedGaussianModel, self).__init__(skewed_gaussian, *args, **kwargs)
- self.set_param_hint('sigma', min=0)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-class DonaichModel(Model):
- __doc__ = donaich.__doc__ + COMMON_DOC if donaich.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(DonaichModel, self).__init__(donaich, *args, **kwargs)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative, ampscale=0.5)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class PowerLawModel(Model):
- __doc__ = powerlaw.__doc__ + COMMON_DOC if powerlaw.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(PowerLawModel, self).__init__(powerlaw, *args, **kwargs)
-
- def guess(self, data, x=None, **kwargs):
- try:
- expon, amp = np.polyfit(np.log(x+1.e-14), np.log(data+1.e-14), 1)
- except:
- expon, amp = 1, np.log(abs(max(data)+1.e-9))
-
- pars = self.make_params(amplitude=np.exp(amp), exponent=expon)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class ExponentialModel(Model):
- __doc__ = exponential.__doc__ + COMMON_DOC if exponential.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(ExponentialModel, self).__init__(exponential, *args, **kwargs)
-
- def guess(self, data, x=None, **kwargs):
- try:
- sval, oval = np.polyfit(x, np.log(abs(data)+1.e-15), 1)
- except:
- sval, oval = 1., np.log(abs(max(data)+1.e-9))
- pars = self.make_params(amplitude=np.exp(oval), decay=-1.0/sval)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class StepModel(Model):
- __doc__ = step.__doc__ + COMMON_DOC if step.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(StepModel, self).__init__(step, *args, **kwargs)
-
- def guess(self, data, x=None, **kwargs):
- if x is None:
- return
- ymin, ymax = min(data), max(data)
- xmin, xmax = min(x), max(x)
- pars = self.make_params(amplitude=(ymax-ymin),
- center=(xmax+xmin)/2.0)
- pars['%ssigma' % self.prefix].set(value=(xmax-xmin)/7.0, min=0.0)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class RectangleModel(Model):
- __doc__ = rectangle.__doc__ + COMMON_DOC if rectangle.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(RectangleModel, self).__init__(rectangle, *args, **kwargs)
- self.set_param_hint('midpoint',
- expr='(%scenter1+%scenter2)/2.0' % (self.prefix,
- self.prefix))
- def guess(self, data, x=None, **kwargs):
- if x is None:
- return
- ymin, ymax = min(data), max(data)
- xmin, xmax = min(x), max(x)
- pars = self.make_params(amplitude=(ymax-ymin),
- center1=(xmax+xmin)/4.0,
- center2=3*(xmax+xmin)/4.0)
- pars['%ssigma1' % self.prefix].set(value=(xmax-xmin)/7.0, min=0.0)
- pars['%ssigma2' % self.prefix].set(value=(xmax-xmin)/7.0, min=0.0)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class ExpressionModel(Model):
- """Model from User-supplied expression
-
-Parameters
-----------
-expr: string of mathematical expression for model.
-independent_vars: list of strings to be set as variable names
-missing: None, 'drop', or 'raise'
- None: Do not check for null or missing values.
- 'drop': Drop null or missing observations in data.
- Use pandas.isnull if pandas is available; otherwise,
- silently fall back to numpy.isnan.
- 'raise': Raise a (more helpful) exception when data contains null
- or missing values.
-prefix: NOT supported for ExpressionModel
-"""
-
- idvar_missing = "No independent variable found in\n %s"
- idvar_notfound = "Cannot find independent variables '%s' in\n %s"
- no_prefix = "ExpressionModel does not support `prefix` argument"
- def __init__(self, expr, independent_vars=None, init_script=None,
- *args, **kwargs):
-
- # create ast evaluator, load custom functions
- self.asteval = Interpreter()
- for name in lineshapes.functions:
- self.asteval.symtable[name] = getattr(lineshapes, name, None)
- if init_script is not None:
- self.asteval.eval(init_script)
-
- # save expr as text, parse to ast, save for later use
- self.expr = expr.strip()
- self.astcode = self.asteval.parse(self.expr)
-
- # find all symbol names found in expression
- sym_names = get_ast_names(self.astcode)
-
- if independent_vars is None and 'x' in sym_names:
- independent_vars = ['x']
- if independent_vars is None:
- raise ValueError(self.idvar_missing % (self.expr))
-
- # determine which named symbols are parameter names,
- # try to find all independent variables
- idvar_found = [False]*len(independent_vars)
- param_names = []
- for name in sym_names:
- if name in independent_vars:
- idvar_found[independent_vars.index(name)] = True
- elif name not in self.asteval.symtable:
- param_names.append(name)
-
- # make sure we have all independent parameters
- if not all(idvar_found):
- lost = []
- for ix, found in enumerate(idvar_found):
- if not found:
- lost.append(independent_vars[ix])
- lost = ', '.join(lost)
- raise ValueError(self.idvar_notfound % (lost, self.expr))
-
- kwargs['independent_vars'] = independent_vars
- if 'prefix' in kwargs:
- raise Warning(self.no_prefix)
-
- def _eval(**kwargs):
- for name, val in kwargs.items():
- self.asteval.symtable[name] = val
- return self.asteval.run(self.astcode)
-
- super(ExpressionModel, self).__init__(_eval, *args, **kwargs)
-
- # set param names here, and other things normally
- # set in _parse_params(), which will be short-circuited.
- self.independent_vars = independent_vars
- self._func_allargs = independent_vars + param_names
- self._param_names = set(param_names)
- self._func_haskeywords = True
- self.def_vals = {}
-
- def __repr__(self):
- return "<lmfit.ExpressionModel('%s')>" % (self.expr)
-
- def _parse_params(self):
- """ExpressionModel._parse_params is over-written (as `pass`)
- to prevent normal parsing of function for parameter names
- """
- pass
+import numpy as np
+from .model import Model
+
+from .lineshapes import (gaussian, lorentzian, voigt, pvoigt, moffat, pearson7,
+ step, rectangle, breit_wigner, logistic,
+ students_t, lognormal, damped_oscillator,
+ expgaussian, skewed_gaussian, donaich,
+ skewed_voigt, exponential, powerlaw, linear,
+ parabolic)
+
+from . import lineshapes
+
+from .asteval import Interpreter
+from .astutils import get_ast_names
+
+class DimensionalError(Exception):
+ pass
+
+def _validate_1d(independent_vars):
+ if len(independent_vars) != 1:
+ raise DimensionalError(
+ "This model requires exactly one independent variable.")
+
+def index_of(arr, val):
+ """return index of array nearest to a value
+ """
+ if val < min(arr):
+ return 0
+ return np.abs(arr-val).argmin()
+
+def fwhm_expr(model):
+ "return constraint expression for fwhm"
+ fmt = "{factor:.7f}*{prefix:s}sigma"
+ return fmt.format(factor=model.fwhm_factor, prefix=model.prefix)
+
+def height_expr(model):
+ "return constraint expression for maximum peak height"
+ fmt = "{factor:.7f}*{prefix:s}amplitude/{prefix:s}sigma"
+ return fmt.format(factor=model.height_factor, prefix=model.prefix)
+
+def guess_from_peak(model, y, x, negative, ampscale=1.0, sigscale=1.0):
+ "estimate amp, cen, sigma for a peak, create params"
+ if x is None:
+ return 1.0, 0.0, 1.0
+ maxy, miny = max(y), min(y)
+ maxx, minx = max(x), min(x)
+ imaxy = index_of(y, maxy)
+ cen = x[imaxy]
+ amp = (maxy - miny)*2.0
+ sig = (maxx-minx)/6.0
+
+ halfmax_vals = np.where(y > (maxy+miny)/2.0)[0]
+ if negative:
+ imaxy = index_of(y, miny)
+ amp = -(maxy - miny)*2.0
+ halfmax_vals = np.where(y < (maxy+miny)/2.0)[0]
+ if len(halfmax_vals) > 2:
+ sig = (x[halfmax_vals[-1]] - x[halfmax_vals[0]])/2.0
+ cen = x[halfmax_vals].mean()
+ amp = amp*sig*ampscale
+ sig = sig*sigscale
+
+ pars = model.make_params(amplitude=amp, center=cen, sigma=sig)
+ pars['%ssigma' % model.prefix].set(min=0.0)
+ return pars
+
+def update_param_vals(pars, prefix, **kwargs):
+ """convenience function to update parameter values
+ with keyword arguments"""
+ for key, val in kwargs.items():
+ pname = "%s%s" % (prefix, key)
+ if pname in pars:
+ pars[pname].value = val
+ return pars
+
+COMMON_DOC = """
+
+Parameters
+----------
+independent_vars: list of strings to be set as variable names
+missing: None, 'drop', or 'raise'
+ None: Do not check for null or missing values.
+ 'drop': Drop null or missing observations in data.
+ Use pandas.isnull if pandas is available; otherwise,
+ silently fall back to numpy.isnan.
+ 'raise': Raise a (more helpful) exception when data contains null
+ or missing values.
+prefix: string to prepend to paramter names, needed to add two Models that
+ have parameter names in common. None by default.
+"""
+
+class ConstantModel(Model):
+ __doc__ = "x -> c" + COMMON_DOC
+ def __init__(self, *args, **kwargs):
+ def constant(x, c):
+ return c
+ super(ConstantModel, self).__init__(constant, *args, **kwargs)
+
+ def guess(self, data, **kwargs):
+ pars = self.make_params()
+ pars['%sc' % self.prefix].set(value=data.mean())
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+class ComplexConstantModel(Model):
+ __doc__ = "x -> re+1j*im" + COMMON_DOC
+ def __init__(self, *args, **kwargs):
+ def constant(x, re, im):
+ return re + 1j*im
+ super(ComplexConstantModel, self).__init__(constant, *args, **kwargs)
+
+ def guess(self, data, **kwargs):
+ pars = self.make_params()
+ pars['%sre' % self.prefix].set(value=data.real.mean())
+ pars['%sim' % self.prefix].set(value=data.imag.mean())
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+class LinearModel(Model):
+ __doc__ = linear.__doc__ + COMMON_DOC if linear.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(LinearModel, self).__init__(linear, *args, **kwargs)
+
+ def guess(self, data, x=None, **kwargs):
+ sval, oval = 0., 0.
+ if x is not None:
+ sval, oval = np.polyfit(x, data, 1)
+ pars = self.make_params(intercept=oval, slope=sval)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class QuadraticModel(Model):
+ __doc__ = parabolic.__doc__ + COMMON_DOC if parabolic.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(QuadraticModel, self).__init__(parabolic, *args, **kwargs)
+
+ def guess(self, data, x=None, **kwargs):
+ a, b, c = 0., 0., 0.
+ if x is not None:
+ a, b, c = np.polyfit(x, data, 2)
+ pars = self.make_params(a=a, b=b, c=c)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+ParabolicModel = QuadraticModel
+
+class PolynomialModel(Model):
+ __doc__ = "x -> c0 + c1 * x + c2 * x**2 + ... c7 * x**7" + COMMON_DOC
+ MAX_DEGREE=7
+ DEGREE_ERR = "degree must be an integer less than %d."
+ def __init__(self, degree, *args, **kwargs):
+ if not isinstance(degree, int) or degree > self.MAX_DEGREE:
+ raise TypeError(self.DEGREE_ERR % self.MAX_DEGREE)
+
+ self.poly_degree = degree
+ pnames = ['c%i' % (i) for i in range(degree + 1)]
+ kwargs['param_names'] = pnames
+
+ def polynomial(x, c0=0, c1=0, c2=0, c3=0, c4=0, c5=0, c6=0, c7=0):
+ return np.polyval([c7, c6, c5, c4, c3, c2, c1, c0], x)
+
+ super(PolynomialModel, self).__init__(polynomial, *args, **kwargs)
+
+ def guess(self, data, x=None, **kwargs):
+ pars = self.make_params()
+ if x is not None:
+ out = np.polyfit(x, data, self.poly_degree)
+ for i, coef in enumerate(out[::-1]):
+ pars['%sc%i'% (self.prefix, i)].set(value=coef)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class GaussianModel(Model):
+ __doc__ = gaussian.__doc__ + COMMON_DOC if gaussian.__doc__ else ""
+ fwhm_factor = 2.354820
+ height_factor = 1./np.sqrt(2*np.pi)
+ def __init__(self, *args, **kwargs):
+ super(GaussianModel, self).__init__(gaussian, *args, **kwargs)
+ self.set_param_hint('sigma', min=0)
+ self.set_param_hint('fwhm', expr=fwhm_expr(self))
+ self.set_param_hint('height', expr=height_expr(self))
+
+ def guess(self, data, x=None, negative=False, **kwargs):
+ pars = guess_from_peak(self, data, x, negative)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class LorentzianModel(Model):
+ __doc__ = lorentzian.__doc__ + COMMON_DOC if lorentzian.__doc__ else ""
+ fwhm_factor = 2.0
+ height_factor = 1./np.pi
+ def __init__(self, *args, **kwargs):
+ super(LorentzianModel, self).__init__(lorentzian, *args, **kwargs)
+ self.set_param_hint('sigma', min=0)
+ self.set_param_hint('fwhm', expr=fwhm_expr(self))
+ self.set_param_hint('height', expr=height_expr(self))
+
+ def guess(self, data, x=None, negative=False, **kwargs):
+ pars = guess_from_peak(self, data, x, negative, ampscale=1.25)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class VoigtModel(Model):
+ __doc__ = voigt.__doc__ + COMMON_DOC if voigt.__doc__ else ""
+ fwhm_factor = 3.60131
+ height_factor = 1./np.sqrt(2*np.pi)
+ def __init__(self, *args, **kwargs):
+ super(VoigtModel, self).__init__(voigt, *args, **kwargs)
+ self.set_param_hint('sigma', min=0)
+ self.set_param_hint('gamma', expr='%ssigma' % self.prefix)
+ self.set_param_hint('fwhm', expr=fwhm_expr(self))
+ self.set_param_hint('height', expr=height_expr(self))
+
+ def guess(self, data, x=None, negative=False, **kwargs):
+ pars = guess_from_peak(self, data, x, negative,
+ ampscale=1.5, sigscale=0.65)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class PseudoVoigtModel(Model):
+ __doc__ = pvoigt.__doc__ + COMMON_DOC if pvoigt.__doc__ else ""
+ fwhm_factor = 2.0
+ def __init__(self, *args, **kwargs):
+ super(PseudoVoigtModel, self).__init__(pvoigt, *args, **kwargs)
+ self.set_param_hint('sigma', min=0)
+ self.set_param_hint('fraction', value=0.5)
+ self.set_param_hint('fwhm', expr=fwhm_expr(self))
+
+ def guess(self, data, x=None, negative=False, **kwargs):
+ pars = guess_from_peak(self, data, x, negative, ampscale=1.25)
+ pars['%sfraction' % self.prefix].set(value=0.5)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class MoffatModel(Model):
+ __doc__ = moffat.__doc__ + COMMON_DOC if moffat.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(MoffatModel, self).__init__(moffat, *args, **kwargs)
+ self.set_param_hint('sigma', min=0)
+ self.set_param_hint('beta')
+ self.set_param_hint('fwhm', expr="2*%ssigma*sqrt(2**(1.0/%sbeta)-1)" % (self.prefix, self.prefix))
+
+ def guess(self, data, x=None, negative=False, **kwargs):
+ pars = guess_from_peak(self, data, x, negative, ampscale=0.5, sigscale=1.)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class Pearson7Model(Model):
+ __doc__ = pearson7.__doc__ + COMMON_DOC if pearson7.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(Pearson7Model, self).__init__(pearson7, *args, **kwargs)
+ self.set_param_hint('expon', value=1.5)
+
+ def guess(self, data, x=None, negative=False, **kwargs):
+ pars = guess_from_peak(self, data, x, negative)
+ pars['%sexpon' % self.prefix].set(value=1.5)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class StudentsTModel(Model):
+ __doc__ = students_t.__doc__ + COMMON_DOC if students_t.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(StudentsTModel, self).__init__(students_t, *args, **kwargs)
+
+ def guess(self, data, x=None, negative=False, **kwargs):
+ pars = guess_from_peak(self, data, x, negative)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class BreitWignerModel(Model):
+ __doc__ = breit_wigner.__doc__ + COMMON_DOC if breit_wigner.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(BreitWignerModel, self).__init__(breit_wigner, *args, **kwargs)
+
+ def guess(self, data, x=None, negative=False, **kwargs):
+ pars = guess_from_peak(self, data, x, negative)
+ pars['%sq' % self.prefix].set(value=1.0)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class LognormalModel(Model):
+ __doc__ = lognormal.__doc__ + COMMON_DOC if lognormal.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(LognormalModel, self).__init__(lognormal, *args, **kwargs)
+
+ def guess(self, data, x=None, negative=False, **kwargs):
+ pars = self.make_params(amplitude=1.0, center=0.0, sigma=0.25)
+ pars['%ssigma' % self.prefix].set(min=0.0)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class DampedOscillatorModel(Model):
+ __doc__ = damped_oscillator.__doc__ + COMMON_DOC if damped_oscillator.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(DampedOscillatorModel, self).__init__(damped_oscillator, *args, **kwargs)
+
+ def guess(self, data, x=None, negative=False, **kwargs):
+ pars =guess_from_peak(self, data, x, negative,
+ ampscale=0.1, sigscale=0.1)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+class ExponentialGaussianModel(Model):
+ __doc__ = expgaussian.__doc__ + COMMON_DOC if expgaussian.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(ExponentialGaussianModel, self).__init__(expgaussian, *args, **kwargs)
+
+ def guess(self, data, x=None, negative=False, **kwargs):
+ pars = guess_from_peak(self, data, x, negative)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+class SkewedGaussianModel(Model):
+ __doc__ = skewed_gaussian.__doc__ + COMMON_DOC if skewed_gaussian.__doc__ else ""
+ fwhm_factor = 2.354820
+ def __init__(self, *args, **kwargs):
+ super(SkewedGaussianModel, self).__init__(skewed_gaussian, *args, **kwargs)
+ self.set_param_hint('sigma', min=0)
+
+ def guess(self, data, x=None, negative=False, **kwargs):
+ pars = guess_from_peak(self, data, x, negative)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+class DonaichModel(Model):
+ __doc__ = donaich.__doc__ + COMMON_DOC if donaich.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(DonaichModel, self).__init__(donaich, *args, **kwargs)
+
+ def guess(self, data, x=None, negative=False, **kwargs):
+ pars = guess_from_peak(self, data, x, negative, ampscale=0.5)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class PowerLawModel(Model):
+ __doc__ = powerlaw.__doc__ + COMMON_DOC if powerlaw.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(PowerLawModel, self).__init__(powerlaw, *args, **kwargs)
+
+ def guess(self, data, x=None, **kwargs):
+ try:
+ expon, amp = np.polyfit(np.log(x+1.e-14), np.log(data+1.e-14), 1)
+ except:
+ expon, amp = 1, np.log(abs(max(data)+1.e-9))
+
+ pars = self.make_params(amplitude=np.exp(amp), exponent=expon)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class ExponentialModel(Model):
+ __doc__ = exponential.__doc__ + COMMON_DOC if exponential.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(ExponentialModel, self).__init__(exponential, *args, **kwargs)
+
+ def guess(self, data, x=None, **kwargs):
+ try:
+ sval, oval = np.polyfit(x, np.log(abs(data)+1.e-15), 1)
+ except:
+ sval, oval = 1., np.log(abs(max(data)+1.e-9))
+ pars = self.make_params(amplitude=np.exp(oval), decay=-1.0/sval)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class StepModel(Model):
+ __doc__ = step.__doc__ + COMMON_DOC if step.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(StepModel, self).__init__(step, *args, **kwargs)
+
+ def guess(self, data, x=None, **kwargs):
+ if x is None:
+ return
+ ymin, ymax = min(data), max(data)
+ xmin, xmax = min(x), max(x)
+ pars = self.make_params(amplitude=(ymax-ymin),
+ center=(xmax+xmin)/2.0)
+ pars['%ssigma' % self.prefix].set(value=(xmax-xmin)/7.0, min=0.0)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class RectangleModel(Model):
+ __doc__ = rectangle.__doc__ + COMMON_DOC if rectangle.__doc__ else ""
+ def __init__(self, *args, **kwargs):
+ super(RectangleModel, self).__init__(rectangle, *args, **kwargs)
+
+ self.set_param_hint('center1')
+ self.set_param_hint('center2')
+ self.set_param_hint('midpoint',
+ expr='(%scenter1+%scenter2)/2.0' % (self.prefix,
+ self.prefix))
+ def guess(self, data, x=None, **kwargs):
+ if x is None:
+ return
+ ymin, ymax = min(data), max(data)
+ xmin, xmax = min(x), max(x)
+ pars = self.make_params(amplitude=(ymax-ymin),
+ center1=(xmax+xmin)/4.0,
+ center2=3*(xmax+xmin)/4.0)
+ pars['%ssigma1' % self.prefix].set(value=(xmax-xmin)/7.0, min=0.0)
+ pars['%ssigma2' % self.prefix].set(value=(xmax-xmin)/7.0, min=0.0)
+ return update_param_vals(pars, self.prefix, **kwargs)
+
+
+class ExpressionModel(Model):
+ """Model from User-supplied expression
+
+Parameters
+----------
+expr: string of mathematical expression for model.
+independent_vars: list of strings to be set as variable names
+missing: None, 'drop', or 'raise'
+ None: Do not check for null or missing values.
+ 'drop': Drop null or missing observations in data.
+ Use pandas.isnull if pandas is available; otherwise,
+ silently fall back to numpy.isnan.
+ 'raise': Raise a (more helpful) exception when data contains null
+ or missing values.
+prefix: NOT supported for ExpressionModel
+"""
+
+ idvar_missing = "No independent variable found in\n %s"
+ idvar_notfound = "Cannot find independent variables '%s' in\n %s"
+ no_prefix = "ExpressionModel does not support `prefix` argument"
+ def __init__(self, expr, independent_vars=None, init_script=None,
+ *args, **kwargs):
+
+ # create ast evaluator, load custom functions
+ self.asteval = Interpreter()
+ for name in lineshapes.functions:
+ self.asteval.symtable[name] = getattr(lineshapes, name, None)
+ if init_script is not None:
+ self.asteval.eval(init_script)
+
+ # save expr as text, parse to ast, save for later use
+ self.expr = expr.strip()
+ self.astcode = self.asteval.parse(self.expr)
+
+ # find all symbol names found in expression
+ sym_names = get_ast_names(self.astcode)
+
+ if independent_vars is None and 'x' in sym_names:
+ independent_vars = ['x']
+ if independent_vars is None:
+ raise ValueError(self.idvar_missing % (self.expr))
+
+ # determine which named symbols are parameter names,
+ # try to find all independent variables
+ idvar_found = [False]*len(independent_vars)
+ param_names = []
+ for name in sym_names:
+ if name in independent_vars:
+ idvar_found[independent_vars.index(name)] = True
+ elif name not in self.asteval.symtable:
+ param_names.append(name)
+
+ # make sure we have all independent parameters
+ if not all(idvar_found):
+ lost = []
+ for ix, found in enumerate(idvar_found):
+ if not found:
+ lost.append(independent_vars[ix])
+ lost = ', '.join(lost)
+ raise ValueError(self.idvar_notfound % (lost, self.expr))
+
+ kwargs['independent_vars'] = independent_vars
+ if 'prefix' in kwargs:
+ raise Warning(self.no_prefix)
+
+ def _eval(**kwargs):
+ for name, val in kwargs.items():
+ self.asteval.symtable[name] = val
+ return self.asteval.run(self.astcode)
+
+ super(ExpressionModel, self).__init__(_eval, *args, **kwargs)
+
+ # set param names here, and other things normally
+ # set in _parse_params(), which will be short-circuited.
+ self.independent_vars = independent_vars
+ self._func_allargs = independent_vars + param_names
+ self._param_names = set(param_names)
+ self._func_haskeywords = True
+ self.def_vals = {}
+
+ def __repr__(self):
+ return "<lmfit.ExpressionModel('%s')>" % (self.expr)
+
+ def _parse_params(self):
+ """ExpressionModel._parse_params is over-written (as `pass`)
+ to prevent normal parsing of function for parameter names
+ """
+ pass
diff --git a/lmfit/ordereddict.py b/lmfit/ordereddict.py
index 524a5c9..2d1d813 100644
--- a/lmfit/ordereddict.py
+++ b/lmfit/ordereddict.py
@@ -1,128 +1,128 @@
-# Copyright (c) 2009 Raymond Hettinger
-#
-# Permission is hereby granted, free of charge, to any person
-# obtaining a copy of this software and associated documentation files
-# (the "Software"), to deal in the Software without restriction,
-# including without limitation the rights to use, copy, modify, merge,
-# publish, distribute, sublicense, and/or sell copies of the Software,
-# and to permit persons to whom the Software is furnished to do so,
-# subject to the following conditions:
-#
-# The above copyright notice and this permission notice shall be
-# included in all copies or substantial portions of the Software.
-#
-# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
-# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
-# OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
-# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
-# HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
-# WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
-# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
-# OTHER DEALINGS IN THE SOFTWARE.
-
-from UserDict import DictMixin
-
-
-class OrderedDict(dict, DictMixin):
-
- def __init__(self, *args, **kwds):
- if len(args) > 1:
- raise TypeError('expected at most 1 arguments, got %d' % len(args))
- try:
- self.__end
- except AttributeError:
- self.clear()
- self.update(*args, **kwds)
-
- def clear(self):
- self.__end = end = []
- end += [None, end, end] # sentinel node for doubly linked list
- self.__map = {} # key --> [key, prev, next]
- dict.clear(self)
-
- def __setitem__(self, key, value):
- if key not in self:
- end = self.__end
- curr = end[1]
- curr[2] = end[1] = self.__map[key] = [key, curr, end]
- dict.__setitem__(self, key, value)
-
- def __delitem__(self, key):
- dict.__delitem__(self, key)
- key, prev, next = self.__map.pop(key)
- prev[2] = next
- next[1] = prev
-
- def __iter__(self):
- end = self.__end
- curr = end[2]
- while curr is not end:
- yield curr[0]
- curr = curr[2]
-
- def __reversed__(self):
- end = self.__end
- curr = end[1]
- while curr is not end:
- yield curr[0]
- curr = curr[1]
-
- def popitem(self, last=True):
- if not self:
- raise KeyError('dictionary is empty')
- if last:
- key = reversed(self).next()
- else:
- key = iter(self).next()
- value = self.pop(key)
- return key, value
-
- def __reduce__(self):
- items = [[k, self[k]] for k in self]
- tmp = self.__map, self.__end
- del self.__map, self.__end
- inst_dict = vars(self).copy()
- self.__map, self.__end = tmp
- if inst_dict:
- return (self.__class__, (items,), inst_dict)
- return self.__class__, (items,)
-
- def keys(self):
- return list(self)
-
- setdefault = DictMixin.setdefault
- update = DictMixin.update
- pop = DictMixin.pop
- values = DictMixin.values
- items = DictMixin.items
- iterkeys = DictMixin.iterkeys
- itervalues = DictMixin.itervalues
- iteritems = DictMixin.iteritems
-
- def __repr__(self):
- if not self:
- return '%s()' % (self.__class__.__name__,)
- return '%s(%r)' % (self.__class__.__name__, self.items())
-
- def copy(self):
- return self.__class__(self)
-
- @classmethod
- def fromkeys(cls, iterable, value=None):
- d = cls()
- for key in iterable:
- d[key] = value
- return d
-
- def __eq__(self, other):
- if isinstance(other, OrderedDict):
- if len(self) != len(other):
- return False
- for p, q in zip(self.items(), other.items()):
- if p != q:
- return False
- return True
- return dict.__eq__(self, other)
-
- def __ne__(self, other):
- return not self == other
+# Copyright (c) 2009 Raymond Hettinger
+#
+# Permission is hereby granted, free of charge, to any person
+# obtaining a copy of this software and associated documentation files
+# (the "Software"), to deal in the Software without restriction,
+# including without limitation the rights to use, copy, modify, merge,
+# publish, distribute, sublicense, and/or sell copies of the Software,
+# and to permit persons to whom the Software is furnished to do so,
+# subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be
+# included in all copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+# OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+# HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+# WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+# OTHER DEALINGS IN THE SOFTWARE.
+
+from UserDict import DictMixin
+
+
+class OrderedDict(dict, DictMixin):
+
+ def __init__(self, *args, **kwds):
+ if len(args) > 1:
+ raise TypeError('expected at most 1 arguments, got %d' % len(args))
+ try:
+ self.__end
+ except AttributeError:
+ self.clear()
+ self.update(*args, **kwds)
+
+ def clear(self):
+ self.__end = end = []
+ end += [None, end, end] # sentinel node for doubly linked list
+ self.__map = {} # key --> [key, prev, next]
+ dict.clear(self)
+
+ def __setitem__(self, key, value):
+ if key not in self:
+ end = self.__end
+ curr = end[1]
+ curr[2] = end[1] = self.__map[key] = [key, curr, end]
+ dict.__setitem__(self, key, value)
+
+ def __delitem__(self, key):
+ dict.__delitem__(self, key)
+ key, prev, next = self.__map.pop(key)
+ prev[2] = next
+ next[1] = prev
+
+ def __iter__(self):
+ end = self.__end
+ curr = end[2]
+ while curr is not end:
+ yield curr[0]
+ curr = curr[2]
+
+ def __reversed__(self):
+ end = self.__end
+ curr = end[1]
+ while curr is not end:
+ yield curr[0]
+ curr = curr[1]
+
+ def popitem(self, last=True):
+ if not self:
+ raise KeyError('dictionary is empty')
+ if last:
+ key = reversed(self).next()
+ else:
+ key = iter(self).next()
+ value = self.pop(key)
+ return key, value
+
+ def __reduce__(self):
+ items = [[k, self[k]] for k in self]
+ tmp = self.__map, self.__end
+ del self.__map, self.__end
+ inst_dict = vars(self).copy()
+ self.__map, self.__end = tmp
+ if inst_dict:
+ return (self.__class__, (items,), inst_dict)
+ return self.__class__, (items,)
+
+ def keys(self):
+ return list(self)
+
+ setdefault = DictMixin.setdefault
+ update = DictMixin.update
+ pop = DictMixin.pop
+ values = DictMixin.values
+ items = DictMixin.items
+ iterkeys = DictMixin.iterkeys
+ itervalues = DictMixin.itervalues
+ iteritems = DictMixin.iteritems
+
+ def __repr__(self):
+ if not self:
+ return '%s()' % (self.__class__.__name__,)
+ return '%s(%r)' % (self.__class__.__name__, self.items())
+
+ def copy(self):
+ return self.__class__(self)
+
+ @classmethod
+ def fromkeys(cls, iterable, value=None):
+ d = cls()
+ for key in iterable:
+ d[key] = value
+ return d
+
+ def __eq__(self, other):
+ if isinstance(other, OrderedDict):
+ if len(self) != len(other):
+ return False
+ for p, q in zip(self.items(), other.items()):
+ if p != q:
+ return False
+ return True
+ return dict.__eq__(self, other)
+
+ def __ne__(self, other):
+ return not self == other
diff --git a/lmfit/parameter.py b/lmfit/parameter.py
index b90d009..0581148 100644
--- a/lmfit/parameter.py
+++ b/lmfit/parameter.py
@@ -1,725 +1,818 @@
-"""
-Parameter class
-"""
-from __future__ import division
-from numpy import arcsin, cos, sin, sqrt, inf, nan
-import json
-from copy import deepcopy
-try:
- from collections import OrderedDict
-except ImportError:
- from ordereddict import OrderedDict
-
-from . import uncertainties
-
-from .asteval import Interpreter
-from .astutils import get_ast_names, valid_symbol_name
-
-
-def check_ast_errors(expr_eval):
- """check for errors derived from asteval"""
- if len(expr_eval.error) > 0:
- expr_eval.raise_exception(None)
-
-
-class Parameters(OrderedDict):
- """
- A dictionary of all the Parameters required to specify a fit model.
-
- All keys must be strings, and valid Python symbol names, and all values
- must be Parameters.
-
- Custom methods:
- ---------------
-
- add()
- add_many()
- dumps() / dump()
- loads() / load()
- """
- def __init__(self, asteval=None, *args, **kwds):
- super(Parameters, self).__init__(self)
- self._asteval = asteval
-
- if asteval is None:
- self._asteval = Interpreter()
- self.update(*args, **kwds)
-
- def __deepcopy__(self, memo):
- _pars = Parameters()
-
- # find the symbols that were added by users, not during construction
- sym_unique = self._asteval.user_defined_symbols()
- unique_symbols = {key: deepcopy(self._asteval.symtable[key], memo)
- for key in sym_unique}
- _pars._asteval.symtable.update(unique_symbols)
-
- # we're just about to add a lot of Parameter objects to the newly
- parameter_list = []
- for key, par in self.items():
- if isinstance(par, Parameter):
- param = Parameter(name=par.name,
- value=par.value,
- min=par.min,
- max=par.max)
- param.vary = par.vary
- param.stderr = par.stderr
- param.correl = par.correl
- param.init_value = par.init_value
- param.expr = par.expr
- parameter_list.append(param)
-
- _pars.add_many(*parameter_list)
-
- return _pars
-
- def __setitem__(self, key, par):
- if key not in self:
- if not valid_symbol_name(key):
- raise KeyError("'%s' is not a valid Parameters name" % key)
- if par is not None and not isinstance(par, Parameter):
- raise ValueError("'%s' is not a Parameter" % par)
- OrderedDict.__setitem__(self, key, par)
- par.name = key
- par._expr_eval = self._asteval
- self._asteval.symtable[key] = par.value
-
- def __add__(self, other):
- "add Parameters objects"
- if not isinstance(other, Parameters):
- raise ValueError("'%s' is not a Parameters object" % other)
- out = deepcopy(self)
- params = other.values()
- out.add_many(*params)
- return out
-
- def __iadd__(self, other):
- """
- add/assign Parameters objects
- """
- if not isinstance(other, Parameters):
- raise ValueError("'%s' is not a Parameters object" % other)
- params = other.values()
- self.add_many(*params)
- return self
-
- def __reduce__(self):
- """
- Required to pickle a Parameters instance.
- """
- # make a list of all the parameters
- params = [self[k] for k in self]
-
- # find the symbols from _asteval.symtable, that need to be remembered.
- sym_unique = self._asteval.user_defined_symbols()
- unique_symbols = {key: deepcopy(self._asteval.symtable[key])
- for key in sym_unique}
-
- return self.__class__, (), {'unique_symbols': unique_symbols,
- 'params': params}
-
- def __setstate__(self, state):
- """
- Unpickle a Parameters instance.
-
- Parameters
- ----------
- state : list
- state[0] is a dictionary containing symbols that need to be
- injected into _asteval.symtable
- state[1:] are the Parameter instances to be added
- is list of parameters
- """
- # first add all the parameters
- self.add_many(*state['params'])
-
- # now update the Interpreter symbol table
- self._asteval.symtable.update(state['unique_symbols'])
-
- def update_constraints(self):
- """
- Update all constrained parameters, checking that dependencies are
- evaluated as needed.
- """
- _updated = [name for name,par in self.items() if par._expr is None]
-
- def _update_param(name):
- """
- Update a parameter value, including setting bounds.
- For a constrained parameter (one with an expr defined),
- this first updates (recursively) all parameters on which
- the parameter depends (using the 'deps' field).
- """
- # Has this param already been updated?
- if name in _updated:
- return
- par = self.__getitem__(name)
- if par._expr_eval is None:
- par._expr_eval = self._asteval
- if par._expr is not None:
- par.expr = par._expr
- if par._expr_ast is not None:
- for dep in par._expr_deps:
- if dep in self.keys():
- _update_param(dep)
- self._asteval.symtable[name] = par.value
- _updated.append(name)
-
- for name in self.keys():
- if name not in _updated:
- _update_param(name)
-
- def pretty_repr(self, oneline=False):
- if oneline:
- return super(Parameters, self).__repr__()
- s = "Parameters({\n"
- for key in self.keys():
- s += " '%s': %s, \n" % (key, self[key])
- s += " })\n"
- return s
-
- def pretty_print(self, oneline=False):
- print(self.pretty_repr(oneline=oneline))
-
- def add(self, name, value=None, vary=True, min=None, max=None, expr=None):
- """
- Convenience function for adding a Parameter:
-
- Example
- -------
- p = Parameters()
- p.add(name, value=XX, ...)
-
- is equivalent to:
- p[name] = Parameter(name=name, value=XX, ....
- """
- if isinstance(name, Parameter):
- self.__setitem__(name.name, name)
- else:
- self.__setitem__(name, Parameter(value=value, name=name, vary=vary,
- min=min, max=max, expr=expr))
-
- def add_many(self, *parlist):
- """
- Convenience function for adding a list of Parameters.
-
- Parameters
- ----------
- parlist : sequence
- A sequence of tuples, or a sequence of `Parameter` instances. If it
- is a sequence of tuples, then each tuple must contain at least the
- name. The order in each tuple is the following:
-
- name, value, vary, min, max, expr
-
- Example
- -------
- p = Parameters()
- # add a sequence of tuples
- p.add_many( (name1, val1, True, None, None, None),
- (name2, val2, True, 0.0, None, None),
- (name3, val3, False, None, None, None),
- (name4, val4))
-
- # add a sequence of Parameter
- f = Parameter('name5', val5)
- g = Parameter('name6', val6)
- p.add_many(f, g)
- """
- for para in parlist:
- if isinstance(para, Parameter):
- self.__setitem__(para.name, para)
- else:
- param = Parameter(*para)
- self.__setitem__(param.name, param)
-
- def valuesdict(self):
- """
- Returns
- -------
- An ordered dictionary of name:value pairs for each Parameter.
- This is distinct from the Parameters itself, as it has values of
- the Parameter values, not the full Parameter object.
- """
-
- return OrderedDict(((p.name, p.value) for p in self.values()))
-
- def dumps(self, **kws):
- """represent Parameters as a JSON string.
-
- all keyword arguments are passed to `json.dumps()`
-
- Returns
- -------
- json string representation of Parameters
-
- See Also
- --------
- dump(), loads(), load(), json.dumps()
- """
- out = [p.__getstate__() for p in self.values()]
- return json.dumps(out, **kws)
-
- def loads(self, s, **kws):
- """load Parameters from a JSON string.
-
- current Parameters will be cleared before loading.
-
- all keyword arguments are passed to `json.loads()`
-
- Returns
- -------
- None. Parameters are updated as a side-effect
-
- See Also
- --------
- dump(), dumps(), load(), json.loads()
-
- """
- self.clear()
- for parstate in json.loads(s, **kws):
- _par = Parameter()
- _par.__setstate__(parstate)
- self.__setitem__(parstate[0], _par)
-
- def dump(self, fp, **kws):
- """write JSON representation of Parameters to a file
- or file-like object (must have a `write()` method).
-
- Arguments
- ---------
- fp open file-like object with `write()` method.
-
- all keyword arguments are passed to `dumps()`
-
- Returns
- -------
- return value from `fp.write()`
-
- See Also
- --------
- dump(), load(), json.dump()
- """
- return fp.write(self.dumps(**kws))
-
- def load(self, fp, **kws):
- """load JSON representation of Parameters from a file
- or file-like object (must have a `read()` method).
-
- Arguments
- ---------
- fp open file-like object with `read()` method.
-
- all keyword arguments are passed to `loads()`
-
- Returns
- -------
- None. Parameters are updated as a side-effect
-
- See Also
- --------
- dump(), loads(), json.load()
- """
- return self.loads(fp.read(), **kws)
-
-
-class Parameter(object):
- """
- A Parameter is an object used to define a Fit Model.
- Attributes
- ----------
- name : str
- Parameter name.
- value : float
- The numerical value of the Parameter.
- vary : bool
- Whether the Parameter is fixed during a fit.
- min : float
- Lower bound for value (None = no lower bound).
- max : float
- Upper bound for value (None = no upper bound).
- expr : str
- An expression specifying constraints for the parameter.
- stderr : float
- The estimated standard error for the best-fit value.
- correl : dict
- Specifies correlation with the other fitted Parameter after a fit.
- Of the form `{'decay': 0.404, 'phase': -0.020, 'frequency': 0.102}`
- """
- def __init__(self, name=None, value=None, vary=True,
- min=None, max=None, expr=None):
- """
- Parameters
- ----------
- name : str, optional
- Name of the parameter.
- value : float, optional
- Numerical Parameter value.
- vary : bool, optional
- Whether the Parameter is fixed during a fit.
- min : float, optional
- Lower bound for value (None = no lower bound).
- max : float, optional
- Upper bound for value (None = no upper bound).
- expr : str, optional
- Mathematical expression used to constrain the value during the fit.
- """
- self.name = name
- self._val = value
- self.user_value = value
- self.init_value = value
- self.min = min
- self.max = max
- self.vary = vary
- self._expr = expr
- self._expr_ast = None
- self._expr_eval = None
- self._expr_deps = []
- self._delay_asteval = False
- self.stderr = None
- self.correl = None
- self.from_internal = lambda val: val
- self._init_bounds()
-
- def set(self, value=None, vary=None, min=None, max=None, expr=None):
- """
- Set or update Parameter attributes.
-
- Parameters
- ----------
- value : float, optional
- Numerical Parameter value.
- vary : bool, optional
- Whether the Parameter is fixed during a fit.
- min : float, optional
- Lower bound for value. To remove a lower bound you must use -np.inf
- max : float, optional
- Upper bound for value. To remove an upper bound you must use np.inf
- expr : str, optional
- Mathematical expression used to constrain the value during the fit.
- To remove a constraint you must supply an empty string.
- """
-
- self.__set_expression(expr)
- if value is not None:
- self._val = value
- if vary is not None:
- self.vary = vary
- if min is not None:
- self.min = min
- if max is not None:
- self.max = max
-
- def _init_bounds(self):
- """make sure initial bounds are self-consistent"""
- #_val is None means - infinity.
- if self._val is not None:
- if self.max is not None and self._val > self.max:
- self._val = self.max
- if self.min is not None and self._val < self.min:
- self._val = self.min
- elif self.min is not None and self._expr is None:
- self._val = self.min
- elif self.max is not None and self._expr is None:
- self._val = self.max
- self.setup_bounds()
-
- def __getstate__(self):
- """get state for pickle"""
- return (self.name, self.value, self.vary, self.expr, self.min,
- self.max, self.stderr, self.correl, self.init_value)
-
- def __setstate__(self, state):
- """set state for pickle"""
- (self.name, self.value, self.vary, self.expr, self.min,
- self.max, self.stderr, self.correl, self.init_value) = state
- self._expr_ast = None
- self._expr_eval = None
- self._expr_deps = []
- self._delay_asteval = False
- self._init_bounds()
-
- def __repr__(self):
- s = []
- if self.name is not None:
- s.append("'%s'" % self.name)
- sval = repr(self._getval())
- if not self.vary and self._expr is None:
- sval = "value=%s (fixed)" % (sval)
- elif self.stderr is not None:
- sval = "value=%s +/- %.3g" % (sval, self.stderr)
- s.append(sval)
- s.append("bounds=[%s:%s]" % (repr(self.min), repr(self.max)))
- if self._expr is not None:
- s.append("expr='%s'" % (self.expr))
- return "<Parameter %s>" % ', '.join(s)
-
- def setup_bounds(self):
- """
- Set up Minuit-style internal/external parameter transformation
- of min/max bounds.
-
- As a side-effect, this also defines the self.from_internal method
- used to re-calculate self.value from the internal value, applying
- the inverse Minuit-style transformation. This method should be
- called prior to passing a Parameter to the user-defined objective
- function.
-
- This code borrows heavily from JJ Helmus' leastsqbound.py
-
- Returns
- -------
- The internal value for parameter from self.value (which holds
- the external, user-expected value). This internal value should
- actually be used in a fit.
- """
- if self.min in (None, -inf) and self.max in (None, inf):
- self.from_internal = lambda val: val
- _val = self._val
- elif self.max in (None, inf):
- self.from_internal = lambda val: self.min - 1.0 + sqrt(val*val + 1)
- _val = sqrt((self._val - self.min + 1.0)**2 - 1)
- elif self.min in (None, -inf):
- self.from_internal = lambda val: self.max + 1 - sqrt(val*val + 1)
- _val = sqrt((self.max - self._val + 1.0)**2 - 1)
- else:
- self.from_internal = lambda val: self.min + (sin(val) + 1) * \
- (self.max - self.min) / 2.0
- _val = arcsin(2*(self._val - self.min)/(self.max - self.min) - 1)
- return _val
-
- def scale_gradient(self, val):
- """
- Returns
- -------
- scaling factor for gradient the according to Minuit-style
- transformation.
- """
- if self.min in (None, -inf) and self.max in (None, inf):
- return 1.0
- elif self.max in (None, inf):
- return val / sqrt(val*val + 1)
- elif self.min in (None, -inf):
- return -val / sqrt(val*val + 1)
- else:
- return cos(val) * (self.max - self.min) / 2.0
-
-
- def _getval(self):
- """get value, with bounds applied"""
-
- # Note assignment to self._val has been changed to self.value
- # The self.value property setter makes sure that the
- # _expr_eval.symtable is kept updated.
- # If you just assign to self._val then
- # _expr_eval.symtable[self.name]
- # becomes stale if parameter.expr is not None.
- if (isinstance(self._val, uncertainties.Variable)
- and self._val is not nan):
- try:
- self.value = self._val.nominal_value
- except AttributeError:
- pass
- if not self.vary and self._expr is None:
- return self._val
- if not hasattr(self, '_expr_eval'):
- self._expr_eval = None
- if not hasattr(self, '_expr_ast'):
- self._expr_ast = None
- if self._expr_ast is None and self._expr is not None:
- self.__set_expression(self._expr)
-
- if self._expr_ast is not None and self._expr_eval is not None:
- if not self._delay_asteval:
- self.value = self._expr_eval(self._expr_ast)
- check_ast_errors(self._expr_eval)
-
- if self.min is None:
- self.min = -inf
- if self.max is None:
- self.max = inf
- if self.max < self.min:
- self.max, self.min = self.min, self.max
- if (abs((1.0 * self.max - self.min)/
- max(abs(self.max), abs(self.min), 1.e-13)) < 1.e-13):
- raise ValueError("Parameter '%s' has min == max" % self.name)
- try:
- self.value = max(self.min, min(self._val, self.max))
- except(TypeError, ValueError):
- self.value = nan
- return self._val
-
- def set_expr_eval(self, evaluator):
- "set expression evaluator instance"
- self._expr_eval = evaluator
-
- @property
- def value(self):
- "The numerical value of the Parameter, with bounds applied"
- return self._getval()
-
- @value.setter
- def value(self, val):
- "Set the numerical Parameter value."
- self._val = val
- if not hasattr(self, '_expr_eval'): self._expr_eval = None
- if self._expr_eval is not None:
- self._expr_eval.symtable[self.name] = val
-
- @property
- def expr(self):
- """
- The mathematical expression used to constrain the value during the fit.
- """
- return self._expr
-
- @expr.setter
- def expr(self, val):
- """
- The mathematical expression used to constrain the value during the fit.
- To remove a constraint you must supply an empty string.
- """
- self.__set_expression(val)
-
- def __set_expression(self, val):
- if val == '':
- val = None
- self._expr = val
- if val is not None:
- self.vary = False
- if not hasattr(self, '_expr_eval'): self._expr_eval = None
- if val is None: self._expr_ast = None
- if val is not None and self._expr_eval is not None:
- self._expr_ast = self._expr_eval.parse(val)
- check_ast_errors(self._expr_eval)
- self._expr_deps = get_ast_names(self._expr_ast)
-
- def __str__(self):
- "string"
- return self.__repr__()
-
- def __abs__(self):
- "abs"
- return abs(self._getval())
-
- def __neg__(self):
- "neg"
- return -self._getval()
-
- def __pos__(self):
- "positive"
- return +self._getval()
-
- def __nonzero__(self):
- "not zero"
- return self._getval() != 0
-
- def __int__(self):
- "int"
- return int(self._getval())
-
- def __long__(self):
- "long"
- return long(self._getval())
-
- def __float__(self):
- "float"
- return float(self._getval())
-
- def __trunc__(self):
- "trunc"
- return self._getval().__trunc__()
-
- def __add__(self, other):
- "+"
- return self._getval() + other
-
- def __sub__(self, other):
- "-"
- return self._getval() - other
-
- def __div__(self, other):
- "/"
- return self._getval() / other
- __truediv__ = __div__
-
- def __floordiv__(self, other):
- "//"
- return self._getval() // other
-
- def __divmod__(self, other):
- "divmod"
- return divmod(self._getval(), other)
-
- def __mod__(self, other):
- "%"
- return self._getval() % other
-
- def __mul__(self, other):
- "*"
- return self._getval() * other
-
- def __pow__(self, other):
- "**"
- return self._getval() ** other
-
- def __gt__(self, other):
- ">"
- return self._getval() > other
-
- def __ge__(self, other):
- ">="
- return self._getval() >= other
-
- def __le__(self, other):
- "<="
- return self._getval() <= other
-
- def __lt__(self, other):
- "<"
- return self._getval() < other
-
- def __eq__(self, other):
- "=="
- return self._getval() == other
- def __ne__(self, other):
- "!="
- return self._getval() != other
-
- def __radd__(self, other):
- "+ (right)"
- return other + self._getval()
-
- def __rdiv__(self, other):
- "/ (right)"
- return other / self._getval()
- __rtruediv__ = __rdiv__
-
- def __rdivmod__(self, other):
- "divmod (right)"
- return divmod(other, self._getval())
-
- def __rfloordiv__(self, other):
- "// (right)"
- return other // self._getval()
-
- def __rmod__(self, other):
- "% (right)"
- return other % self._getval()
-
- def __rmul__(self, other):
- "* (right)"
- return other * self._getval()
-
- def __rpow__(self, other):
- "** (right)"
- return other ** self._getval()
-
- def __rsub__(self, other):
- "- (right)"
- return other - self._getval()
-
-def isParameter(x):
- "test for Parameter-ness"
- return (isinstance(x, Parameter) or
- x.__class__.__name__ == 'Parameter')
+"""
+Parameter class
+"""
+from __future__ import division
+from numpy import arcsin, cos, sin, sqrt, inf, nan, isfinite
+import json
+from copy import deepcopy
+try:
+ from collections import OrderedDict
+except ImportError:
+ from ordereddict import OrderedDict
+
+from . import uncertainties
+
+from .asteval import Interpreter
+from .astutils import get_ast_names, valid_symbol_name
+
+
+def check_ast_errors(expr_eval):
+ """check for errors derived from asteval"""
+ if len(expr_eval.error) > 0:
+ expr_eval.raise_exception(None)
+
+
+def isclose(x, y, rtol=1e-5, atol=1e-8):
+ """
+ The truth whether two numbers are the same, within an absolute and
+ relative tolerance.
+
+ i.e. abs(`x` - `y`) <= (`atol` + `rtol` * absolute(`y`))
+
+ Parameters
+ ----------
+ x, y : float
+ Input values
+ rtol : float
+ The relative tolerance parameter (see Notes).
+ atol : float
+ The absolute tolerance parameter (see Notes).
+
+ Returns
+ -------
+ y : bool
+ Are `x` and `x` are equal within tolerance?
+ """
+ def within_tol(x, y, atol, rtol):
+ return abs(x - y) <= atol + rtol * abs(y)
+
+ xfin = isfinite(x)
+ yfin = isfinite(y)
+
+ # both are finite
+ if xfin and yfin:
+ return within_tol(x, y, atol, rtol)
+ elif x == y:
+ return True
+ else:
+ return False
+
+
+class Parameters(OrderedDict):
+ """
+ A dictionary of all the Parameters required to specify a fit model.
+
+ All keys must be strings, and valid Python symbol names, and all values
+ must be Parameters.
+
+ Custom methods:
+ ---------------
+
+ add()
+ add_many()
+ dumps() / dump()
+ loads() / load()
+ """
+ def __init__(self, asteval=None, *args, **kwds):
+ super(Parameters, self).__init__(self)
+ self._asteval = asteval
+
+ if asteval is None:
+ self._asteval = Interpreter()
+ self.update(*args, **kwds)
+
+ def copy(self):
+ """Parameters.copy() should always be a deepcopy"""
+ return self.__deepcopy__(None)
+
+ def __copy__(self, memo):
+ """Parameters.copy() should always be a deepcopy"""
+ self.__deepcopy__(memo)
+
+ def __deepcopy__(self, memo):
+ """Parameters deepcopy needs to make sure that
+ asteval is available and that all individula
+ parameter objects are copied"""
+ _pars = Parameters(asteval=None)
+
+ # find the symbols that were added by users, not during construction
+ sym_unique = self._asteval.user_defined_symbols()
+ unique_symbols = {key: deepcopy(self._asteval.symtable[key], memo)
+ for key in sym_unique}
+ _pars._asteval.symtable.update(unique_symbols)
+
+ # we're just about to add a lot of Parameter objects to the newly
+ parameter_list = []
+ for key, par in self.items():
+ if isinstance(par, Parameter):
+ param = Parameter(name=par.name,
+ value=par.value,
+ min=par.min,
+ max=par.max)
+ param.vary = par.vary
+ param.stderr = par.stderr
+ param.correl = par.correl
+ param.init_value = par.init_value
+ param.expr = par.expr
+ parameter_list.append(param)
+
+ _pars.add_many(*parameter_list)
+
+ return _pars
+
+ def __setitem__(self, key, par):
+ if key not in self:
+ if not valid_symbol_name(key):
+ raise KeyError("'%s' is not a valid Parameters name" % key)
+ if par is not None and not isinstance(par, Parameter):
+ raise ValueError("'%s' is not a Parameter" % par)
+ OrderedDict.__setitem__(self, key, par)
+ par.name = key
+ par._expr_eval = self._asteval
+ self._asteval.symtable[key] = par.value
+
+ def __add__(self, other):
+ """
+ Add Parameters objects
+ """
+ if not isinstance(other, Parameters):
+ raise ValueError("'%s' is not a Parameters object" % other)
+ out = deepcopy(self)
+ params = other.values()
+ out.add_many(*params)
+ return out
+
+ def __iadd__(self, other):
+ """
+ Add/assign Parameters objects
+ """
+ if not isinstance(other, Parameters):
+ raise ValueError("'%s' is not a Parameters object" % other)
+ params = other.values()
+ self.add_many(*params)
+ return self
+
+ def __reduce__(self):
+ """
+ Required to pickle a Parameters instance.
+ """
+ # make a list of all the parameters
+ params = [self[k] for k in self]
+
+ # find the symbols from _asteval.symtable, that need to be remembered.
+ sym_unique = self._asteval.user_defined_symbols()
+ unique_symbols = {key: deepcopy(self._asteval.symtable[key])
+ for key in sym_unique}
+
+ return self.__class__, (), {'unique_symbols': unique_symbols,
+ 'params': params}
+
+ def __setstate__(self, state):
+ """
+ Unpickle a Parameters instance.
+
+ Parameters
+ ----------
+ state : dict
+ state['unique_symbols'] is a dictionary containing symbols that
+ need to be injected into _asteval.symtable
+ state['params'] is a list of Parameter instances to be added
+ """
+ # first update the Interpreter symbol table. This needs to be done
+ # first because Parameter's early in the list may depend on later
+ # Parameter's. This leads to problems because add_many eventually leads
+ # to a Parameter value being retrieved with _getval, which, if the
+ # dependent value hasn't already been added to the symtable, leads to
+ # an Error. Another way of doing this would be to remove all the expr
+ # from the Parameter instances before they get added, then to restore
+ # them.
+ self._asteval.symtable.update(state['unique_symbols'])
+
+ # then add all the parameters
+ self.add_many(*state['params'])
+
+
+ def update_constraints(self):
+ """
+ Update all constrained parameters, checking that dependencies are
+ evaluated as needed.
+ """
+ requires_update = {name for name, par in self.items()
+ if par._expr is not None}
+ updated_tracker = set(requires_update)
+
+ def _update_param(name):
+ """
+ Update a parameter value, including setting bounds.
+ For a constrained parameter (one with an expr defined),
+ this first updates (recursively) all parameters on which
+ the parameter depends (using the 'deps' field).
+ """
+ par = self.__getitem__(name)
+ if par._expr_eval is None:
+ par._expr_eval = self._asteval
+ for dep in par._expr_deps:
+ if dep in updated_tracker:
+ _update_param(dep)
+ self._asteval.symtable[name] = par.value
+ updated_tracker.discard(name)
+
+ for name in requires_update:
+ _update_param(name)
+
+ def pretty_repr(self, oneline=False):
+ if oneline:
+ return super(Parameters, self).__repr__()
+ s = "Parameters({\n"
+ for key in self.keys():
+ s += " '%s': %s, \n" % (key, self[key])
+ s += " })\n"
+ return s
+
+ def pretty_print(self, oneline=False, colwidth=8, precision=4, fmt='g',
+ columns=['value', 'min', 'max', 'stderr', 'vary', 'expr']):
+ """Pretty-print parameters data.
+
+ Parameters
+ ----------
+ oneline : boolean
+ If True prints a one-line parameters representation. Default False.
+ colwidth : int
+ column width for all except the first (i.e. name) column.
+ columns : list of strings
+ list of columns names to print. All values must be valid
+ :class:`Parameter` attributes.
+ precision : int
+ number of digits to be printed after floating point.
+ format : string
+ single-char numeric formatter. Valid values: 'f' floating point,
+ 'g' floating point and exponential, 'e' exponential.
+ """
+ if oneline:
+ print(self.pretty_repr(oneline=oneline))
+ return
+
+ name_len = max(len(s) for s in self)
+ allcols = ['name'] + columns
+ title = '{:{name_len}} ' + len(columns) * ' {:>{n}}'
+ print(title.format(*allcols, name_len=name_len, n=colwidth).title())
+ numstyle = '{%s:>{n}.{p}{f}}' # format for numeric columns
+ otherstyles = dict(name='{name:<{name_len}} ', stderr='{stderr!s:>{n}}',
+ vary='{vary!s:>{n}}', expr='{expr!s:>{n}}')
+ line = ' '.join([otherstyles.get(k, numstyle % k) for k in allcols])
+ for name, values in sorted(self.items()):
+ pvalues = {k: getattr(values, k) for k in columns}
+ pvalues['name'] = name
+ # stderr is a special case: it is either numeric or None (i.e. str)
+ if 'stderr' in columns and pvalues['stderr'] is not None:
+ pvalues['stderr'] = (numstyle % '').format(
+ pvalues['stderr'], n=colwidth, p=precision, f=fmt)
+ print(line.format(name_len=name_len, n=colwidth, p=precision, f=fmt,
+ **pvalues))
+
+ def add(self, name, value=None, vary=True, min=-inf, max=inf, expr=None):
+ """
+ Convenience function for adding a Parameter:
+
+ Example
+ -------
+ p = Parameters()
+ p.add(name, value=XX, ...)
+
+ is equivalent to:
+ p[name] = Parameter(name=name, value=XX, ....
+ """
+ if isinstance(name, Parameter):
+ self.__setitem__(name.name, name)
+ else:
+ self.__setitem__(name, Parameter(value=value, name=name, vary=vary,
+ min=min, max=max, expr=expr))
+
+ def add_many(self, *parlist):
+ """
+ Convenience function for adding a list of Parameters.
+
+ Parameters
+ ----------
+ parlist : sequence
+ A sequence of tuples, or a sequence of `Parameter` instances. If it
+ is a sequence of tuples, then each tuple must contain at least the
+ name. The order in each tuple is the following:
+
+ name, value, vary, min, max, expr
+
+ Example
+ -------
+ p = Parameters()
+ # add a sequence of tuples
+ p.add_many( (name1, val1, True, None, None, None),
+ (name2, val2, True, 0.0, None, None),
+ (name3, val3, False, None, None, None),
+ (name4, val4))
+
+ # add a sequence of Parameter
+ f = Parameter('name5', val5)
+ g = Parameter('name6', val6)
+ p.add_many(f, g)
+ """
+ for para in parlist:
+ if isinstance(para, Parameter):
+ self.__setitem__(para.name, para)
+ else:
+ param = Parameter(*para)
+ self.__setitem__(param.name, param)
+
+ def valuesdict(self):
+ """
+ Returns
+ -------
+ An ordered dictionary of name:value pairs for each Parameter.
+ This is distinct from the Parameters itself, as it has values of
+ the Parameter values, not the full Parameter object.
+ """
+
+ return OrderedDict(((p.name, p.value) for p in self.values()))
+
+ def dumps(self, **kws):
+ """represent Parameters as a JSON string.
+
+ all keyword arguments are passed to `json.dumps()`
+
+ Returns
+ -------
+ json string representation of Parameters
+
+ See Also
+ --------
+ dump(), loads(), load(), json.dumps()
+ """
+ out = [p.__getstate__() for p in self.values()]
+ return json.dumps(out, **kws)
+
+ def loads(self, s, **kws):
+ """load Parameters from a JSON string.
+
+ current Parameters will be cleared before loading.
+
+ all keyword arguments are passed to `json.loads()`
+
+ Returns
+ -------
+ None. Parameters are updated as a side-effect
+
+ See Also
+ --------
+ dump(), dumps(), load(), json.loads()
+
+ """
+ self.clear()
+ for parstate in json.loads(s, **kws):
+ _par = Parameter()
+ _par.__setstate__(parstate)
+ self.__setitem__(parstate[0], _par)
+
+ def dump(self, fp, **kws):
+ """write JSON representation of Parameters to a file
+ or file-like object (must have a `write()` method).
+
+ Arguments
+ ---------
+ fp open file-like object with `write()` method.
+
+ all keyword arguments are passed to `dumps()`
+
+ Returns
+ -------
+ return value from `fp.write()`
+
+ See Also
+ --------
+ dump(), load(), json.dump()
+ """
+ return fp.write(self.dumps(**kws))
+
+ def load(self, fp, **kws):
+ """load JSON representation of Parameters from a file
+ or file-like object (must have a `read()` method).
+
+ Arguments
+ ---------
+ fp open file-like object with `read()` method.
+
+ all keyword arguments are passed to `loads()`
+
+ Returns
+ -------
+ None. Parameters are updated as a side-effect
+
+ See Also
+ --------
+ dump(), loads(), json.load()
+ """
+ return self.loads(fp.read(), **kws)
+
+
+class Parameter(object):
+ """
+ A Parameter is an object used to define a Fit Model.
+ Attributes
+ ----------
+ name : str
+ Parameter name.
+ value : float
+ The numerical value of the Parameter.
+ vary : bool
+ Whether the Parameter is fixed during a fit.
+ min : float
+ Lower bound for value (None or -inf means no lower bound).
+ max : float
+ Upper bound for value (None or inf means no upper bound).
+ expr : str
+ An expression specifying constraints for the parameter.
+ stderr : float
+ The estimated standard error for the best-fit value.
+ correl : dict
+ Specifies correlation with the other fitted Parameter after a fit.
+ Of the form `{'decay': 0.404, 'phase': -0.020, 'frequency': 0.102}`
+ """
+ def __init__(self, name=None, value=None, vary=True,
+ min=-inf, max=inf, expr=None):
+ """
+ Parameters
+ ----------
+ name : str, optional
+ Name of the parameter.
+ value : float, optional
+ Numerical Parameter value.
+ vary : bool, optional
+ Whether the Parameter is fixed during a fit.
+ min : float, optional
+ Lower bound for value (None or -inf means no lower bound).
+ max : float, optional
+ Upper bound for value (None or inf means no upper bound).
+ expr : str, optional
+ Mathematical expression used to constrain the value during the fit.
+ """
+ self.name = name
+ self._val = value
+ self.user_value = value
+ self.init_value = value
+ self.min = min
+ self.max = max
+ self.vary = vary
+ self._expr = expr
+ self._expr_ast = None
+ self._expr_eval = None
+ self._expr_deps = []
+ self._delay_asteval = False
+ self.stderr = None
+ self.correl = None
+ self.from_internal = lambda val: val
+ self._init_bounds()
+
+ def set(self, value=None, vary=None, min=-inf, max=inf, expr=None):
+ """
+ Set or update Parameter attributes.
+
+ Parameters
+ ----------
+ value : float, optional
+ Numerical Parameter value.
+ vary : bool, optional
+ Whether the Parameter is fixed during a fit.
+ min : float, optional
+ Lower bound for value. To remove a lower bound you must use -np.inf
+ max : float, optional
+ Upper bound for value. To remove an upper bound you must use np.inf
+ expr : str, optional
+ Mathematical expression used to constrain the value during the fit.
+ To remove a constraint you must supply an empty string.
+ """
+
+ self.__set_expression(expr)
+ if value is not None:
+ self._val = value
+ if vary is not None:
+ self.vary = vary
+ if min is None:
+ min = -inf
+ if max is None:
+ max = inf
+ self.min = min
+ self.max = max
+
+ def _init_bounds(self):
+ """make sure initial bounds are self-consistent"""
+ # _val is None means - infinity.
+ if self.max is None:
+ self.max = inf
+ if self.min is None:
+ self.min = -inf
+ if self._val is not None:
+ if self.min > self.max:
+ self.min, self.max = self.max, self.min
+ if isclose(self.min, self.max, atol=1e-13, rtol=1e-13):
+ raise ValueError("Parameter '%s' has min == max" % self.name)
+
+ if self._val > self.max:
+ self._val = self.max
+ if self._val < self.min:
+ self._val = self.min
+ elif self._expr is None:
+ self._val = self.min
+ self.setup_bounds()
+
+ def __getstate__(self):
+ """get state for pickle"""
+ return (self.name, self.value, self.vary, self.expr, self.min,
+ self.max, self.stderr, self.correl, self.init_value)
+
+ def __setstate__(self, state):
+ """set state for pickle"""
+ (self.name, self.value, self.vary, self.expr, self.min,
+ self.max, self.stderr, self.correl, self.init_value) = state
+ self._expr_ast = None
+ self._expr_eval = None
+ self._expr_deps = []
+ self._delay_asteval = False
+ self._init_bounds()
+
+ def __repr__(self):
+ s = []
+ if self.name is not None:
+ s.append("'%s'" % self.name)
+ sval = repr(self._getval())
+ if not self.vary and self._expr is None:
+ sval = "value=%s (fixed)" % sval
+ elif self.stderr is not None:
+ sval = "value=%s +/- %.3g" % (sval, self.stderr)
+ s.append(sval)
+ s.append("bounds=[%s:%s]" % (repr(self.min), repr(self.max)))
+ if self._expr is not None:
+ s.append("expr='%s'" % self.expr)
+ return "<Parameter %s>" % ', '.join(s)
+
+ def setup_bounds(self):
+ """
+ Set up Minuit-style internal/external parameter transformation
+ of min/max bounds.
+
+ As a side-effect, this also defines the self.from_internal method
+ used to re-calculate self.value from the internal value, applying
+ the inverse Minuit-style transformation. This method should be
+ called prior to passing a Parameter to the user-defined objective
+ function.
+
+ This code borrows heavily from JJ Helmus' leastsqbound.py
+
+ Returns
+ -------
+ The internal value for parameter from self.value (which holds
+ the external, user-expected value). This internal value should
+ actually be used in a fit.
+ """
+ if self.min is None:
+ self.min = -inf
+ if self.max is None:
+ self.max = inf
+ if self.min == -inf and self.max == inf:
+ self.from_internal = lambda val: val
+ _val = self._val
+ elif self.max == inf:
+ self.from_internal = lambda val: self.min - 1.0 + sqrt(val*val + 1)
+ _val = sqrt((self._val - self.min + 1.0)**2 - 1)
+ elif self.min == -inf:
+ self.from_internal = lambda val: self.max + 1 - sqrt(val*val + 1)
+ _val = sqrt((self.max - self._val + 1.0)**2 - 1)
+ else:
+ self.from_internal = lambda val: self.min + (sin(val) + 1) * \
+ (self.max - self.min) / 2.0
+ _val = arcsin(2*(self._val - self.min)/(self.max - self.min) - 1)
+ return _val
+
+ def scale_gradient(self, val):
+ """
+ Returns
+ -------
+ scaling factor for gradient the according to Minuit-style
+ transformation.
+ """
+ if self.min == -inf and self.max == inf:
+ return 1.0
+ elif self.max == inf:
+ return val / sqrt(val*val + 1)
+ elif self.min == -inf:
+ return -val / sqrt(val*val + 1)
+ else:
+ return cos(val) * (self.max - self.min) / 2.0
+
+ def _getval(self):
+ """get value, with bounds applied"""
+
+ # Note assignment to self._val has been changed to self.value
+ # The self.value property setter makes sure that the
+ # _expr_eval.symtable is kept updated.
+ # If you just assign to self._val then
+ # _expr_eval.symtable[self.name]
+ # becomes stale if parameter.expr is not None.
+ if (isinstance(self._val, uncertainties.Variable)
+ and self._val is not nan):
+ try:
+ self.value = self._val.nominal_value
+ except AttributeError:
+ pass
+ if not self.vary and self._expr is None:
+ return self._val
+
+ if self._expr is not None:
+ if self._expr_ast is None:
+ self.__set_expression(self._expr)
+
+ if self._expr_eval is not None:
+ if not self._delay_asteval:
+ self.value = self._expr_eval(self._expr_ast)
+ check_ast_errors(self._expr_eval)
+
+ v = self._val
+ if v > self.max: v = self.max
+ if v < self.min: v = self.min
+ self.value = self._val = v
+ return self._val
+
+ def set_expr_eval(self, evaluator):
+ """set expression evaluator instance"""
+ self._expr_eval = evaluator
+
+ @property
+ def value(self):
+ """The numerical value of the Parameter, with bounds applied"""
+ return self._getval()
+
+ @value.setter
+ def value(self, val):
+ """
+ Set the numerical Parameter value.
+ """
+ self._val = val
+ if not hasattr(self, '_expr_eval'):
+ self._expr_eval = None
+ if self._expr_eval is not None:
+ self._expr_eval.symtable[self.name] = val
+
+ @property
+ def expr(self):
+ """
+ The mathematical expression used to constrain the value during the fit.
+ """
+ return self._expr
+
+ @expr.setter
+ def expr(self, val):
+ """
+ The mathematical expression used to constrain the value during the fit.
+ To remove a constraint you must supply an empty string.
+ """
+ self.__set_expression(val)
+
+ def __set_expression(self, val):
+ if val == '':
+ val = None
+ self._expr = val
+ if val is not None:
+ self.vary = False
+ if not hasattr(self, '_expr_eval'):
+ self._expr_eval = None
+ if val is None:
+ self._expr_ast = None
+ if val is not None and self._expr_eval is not None:
+ self._expr_ast = self._expr_eval.parse(val)
+ check_ast_errors(self._expr_eval)
+ self._expr_deps = get_ast_names(self._expr_ast)
+
+ def __str__(self):
+ """string"""
+ return self.__repr__()
+
+ def __abs__(self):
+ """abs"""
+ return abs(self._getval())
+
+ def __neg__(self):
+ """neg"""
+ return -self._getval()
+
+ def __pos__(self):
+ """positive"""
+ return +self._getval()
+
+ def __nonzero__(self):
+ """not zero"""
+ return self._getval() != 0
+
+ def __int__(self):
+ """int"""
+ return int(self._getval())
+
+ def __float__(self):
+ """float"""
+ return float(self._getval())
+
+ def __trunc__(self):
+ """trunc"""
+ return self._getval().__trunc__()
+
+ def __add__(self, other):
+ """+"""
+ return self._getval() + other
+
+ def __sub__(self, other):
+ """-"""
+ return self._getval() - other
+
+ def __div__(self, other):
+ """/"""
+ return self._getval() / other
+ __truediv__ = __div__
+
+ def __floordiv__(self, other):
+ """//"""
+ return self._getval() // other
+
+ def __divmod__(self, other):
+ """divmod"""
+ return divmod(self._getval(), other)
+
+ def __mod__(self, other):
+ """%"""
+ return self._getval() % other
+
+ def __mul__(self, other):
+ """*"""
+ return self._getval() * other
+
+ def __pow__(self, other):
+ """**"""
+ return self._getval() ** other
+
+ def __gt__(self, other):
+ """>"""
+ return self._getval() > other
+
+ def __ge__(self, other):
+ """>="""
+ return self._getval() >= other
+
+ def __le__(self, other):
+ """<="""
+ return self._getval() <= other
+
+ def __lt__(self, other):
+ """<"""
+ return self._getval() < other
+
+ def __eq__(self, other):
+ """=="""
+ return self._getval() == other
+
+ def __ne__(self, other):
+ """!="""
+ return self._getval() != other
+
+ def __radd__(self, other):
+ """+ (right)"""
+ return other + self._getval()
+
+ def __rdiv__(self, other):
+ """/ (right)"""
+ return other / self._getval()
+ __rtruediv__ = __rdiv__
+
+ def __rdivmod__(self, other):
+ """divmod (right)"""
+ return divmod(other, self._getval())
+
+ def __rfloordiv__(self, other):
+ """// (right)"""
+ return other // self._getval()
+
+ def __rmod__(self, other):
+ """% (right)"""
+ return other % self._getval()
+
+ def __rmul__(self, other):
+ """* (right)"""
+ return other * self._getval()
+
+ def __rpow__(self, other):
+ """** (right)"""
+ return other ** self._getval()
+
+ def __rsub__(self, other):
+ """- (right)"""
+ return other - self._getval()
+
+
+def isParameter(x):
+ """Test for Parameter-ness"""
+ return (isinstance(x, Parameter) or
+ x.__class__.__name__ == 'Parameter')
diff --git a/lmfit/printfuncs.py b/lmfit/printfuncs.py
index 76537bc..4b279b0 100644
--- a/lmfit/printfuncs.py
+++ b/lmfit/printfuncs.py
@@ -1,227 +1,229 @@
-# -*- coding: utf-8 -*-
-"""
-Created on Fri Apr 20 19:24:21 2012
-
- at author: Tillsten
-
-Changes:
- - 13-Feb-2013 M Newville
- complemented "report_errors" and "report_ci" with
- "error_report" and "ci_report" (respectively) which
- return the text of the report. Thus report_errors()
- is simply:
- def report_errors(params, modelpars=None, show_correl=True):
- print error_report(params, modelpars=modelpars,
- show_correl=show_correl)
- and similar for report_ci() / ci_report()
-
-"""
-
-from __future__ import print_function
-from .parameter import Parameters
-import re
-
-def alphanumeric_sort(s, _nsre=re.compile('([0-9]+)')):
- return [int(text) if text.isdigit() else text.lower()
- for text in re.split(_nsre, s)]
-
-def getfloat_attr(obj, attr, fmt='%.3f'):
- "format an attribute of an object for printing"
- val = getattr(obj, attr, None)
- if val is None:
- return 'unknown'
- if isinstance(val, int):
- return '%d' % val
- if isinstance(val, float):
- return fmt % val
- else:
- return repr(val)
-
-def gformat(val, length=11):
- """format a number with '%g'-like format, except that
- the return will be length ``length`` (default=12)
- and have at least length-6 significant digits
- """
- length = max(length, 7)
- fmt = '{: .%ig}' % (length-6)
- if isinstance(val, int):
- out = ('{: .%ig}' % (length-2)).format(val)
- if len(out) > length:
- out = fmt.format(val)
- else:
- out = fmt.format(val)
- if len(out) < length:
- if 'e' in out:
- ie = out.find('e')
- if '.' not in out[:ie]:
- out = out[:ie] + '.' + out[ie:]
- out = out.replace('e', '0'*(length-len(out))+'e')
- else:
- fmt = '{: .%ig}' % (length-1)
- out = fmt.format(val)[:length]
- if len(out) < length:
- pad = '0' if '.' in out else ' '
- out += pad*(length-len(out))
- return out
-
-CORREL_HEAD = '[[Correlations]] (unreported correlations are < % .3f)'
-
-def fit_report(inpars, modelpars=None, show_correl=True, min_correl=0.1,
- sort_pars=False):
- """return text of a report for fitted params best-fit values,
- uncertainties and correlations
-
- arguments
- ----------
- inpars Parameters from fit or Minizer object returned from a fit.
- modelpars Optional Known Model Parameters [None]
- show_correl whether to show list of sorted correlations [True]
- min_correl smallest correlation absolute value to show [0.1]
- sort_pars If True, then fit_report will show parameter names
- sorted in alphanumerical order. If False, then the
- parameters will be listed in the order they were added to
- the Parameters dictionary. If sort_pars is callable, then
- this (one argument) function is used to extract a
- comparison key from each list element.
- """
- if isinstance(inpars, Parameters):
- result, params = None, inpars
- if hasattr(inpars, 'params'):
- result = inpars
- params = inpars.params
-
- if sort_pars:
- if callable(sort_pars):
- key = sort_pars
- else:
- key = alphanumeric_sort
- parnames = sorted(params, key=key)
- else:
- # dict.keys() returns a KeysView in py3, and they're indexed further
- # down
- parnames = list(params.keys())
-
- buff = []
- add = buff.append
- if result is not None:
- add("[[Fit Statistics]]")
- add(" # function evals = %s" % getfloat_attr(result, 'nfev'))
- add(" # data points = %s" % getfloat_attr(result, 'ndata'))
- add(" # variables = %s" % getfloat_attr(result, 'nvarys'))
- add(" chi-square = %s" % getfloat_attr(result, 'chisqr'))
- add(" reduced chi-square = %s" % getfloat_attr(result, 'redchi'))
-
- namelen = max([len(n) for n in parnames])
- add("[[Variables]]")
- for name in parnames:
- par = params[name]
- space = ' '*(namelen+1-len(name))
- nout = "%s:%s" % (name, space)
- inval = '(init= ?)'
- if par.init_value is not None:
- inval = '(init=% .7g)' % par.init_value
- if modelpars is not None and name in modelpars:
- inval = '%s, model_value =% .7g' % (inval, modelpars[name].value)
- try:
- sval = gformat(par.value)
- except (TypeError, ValueError):
- sval = 'Non Numeric Value?'
-
- if par.stderr is not None:
- serr = gformat(par.stderr, length=9)
-
- try:
- spercent = '({:.2%})'.format(abs(par.stderr/par.value))
- except ZeroDivisionError:
- spercent = ''
- sval = '%s +/-%s %s' % (sval, serr, spercent)
-
- if par.vary:
- add(" %s %s %s" % (nout, sval, inval))
- elif par.expr is not None:
- add(" %s %s == '%s'" % (nout, sval, par.expr))
- else:
- add(" %s % .7g (fixed)" % (nout, par.value))
-
- if show_correl:
- add(CORREL_HEAD % min_correl)
- correls = {}
- for i, name in enumerate(parnames):
- par = params[name]
- if not par.vary:
- continue
- if hasattr(par, 'correl') and par.correl is not None:
- for name2 in parnames[i+1:]:
- if (name != name2 and name2 in par.correl and
- abs(par.correl[name2]) > min_correl):
- correls["%s, %s" % (name, name2)] = par.correl[name2]
-
- sort_correl = sorted(correls.items(), key=lambda it: abs(it[1]))
- sort_correl.reverse()
- for name, val in sort_correl:
- lspace = max(1, 25 - len(name))
- add(' C(%s)%s = % .3f ' % (name, (' '*30)[:lspace], val))
- return '\n'.join(buff)
-
-
-def report_errors(params, **kws):
- """print a report for fitted params: see error_report()"""
- print(fit_report(params, **kws))
-
-
-def report_fit(params, **kws):
- """print a report for fitted params: see error_report()"""
- print(fit_report(params, **kws))
-
-
-def ci_report(ci, with_offset=True, ndigits=5):
- """return text of a report for confidence intervals
-
- Parameters
- ----------
- with_offset : bool (default `True`)
- whether to subtract best value from all other values.
- ndigits : int (default 5)
- number of significant digits to show
-
- Returns
- -------
- text of formatted report on confidence intervals.
- """
- maxlen = max([len(i) for i in ci])
- buff = []
- add = buff.append
- def convp(x):
- if abs(x[0]) < 1.e-2:
- return "_BEST_"
- return "%.2f%%" % (x[0]*100)
-
- title_shown = False
- fmt_best = fmt_diff = "{0:.%if}" % ndigits
- if with_offset:
- fmt_diff = "{0:+.%if}" % ndigits
- for name, row in ci.items():
- if not title_shown:
- add("".join([''.rjust(maxlen+1)]+[i.rjust(ndigits+5)
- for i in map(convp, row)]))
- title_shown = True
- thisrow = [" %s:" % name.ljust(maxlen)]
- offset = 0.0
- if with_offset:
- for cval, val in row:
- if abs(cval) < 1.e-2:
- offset = val
- for cval, val in row:
- if cval < 1.e-2:
- sval = fmt_best.format(val)
- else:
- sval = fmt_diff.format(val-offset)
- thisrow.append(sval.rjust(ndigits+5))
- add("".join(thisrow))
-
- return '\n'.join(buff)
-
-
-def report_ci(ci):
- """print a report for confidence intervals"""
- print(ci_report(ci))
+# -*- coding: utf-8 -*-
+"""
+Created on Fri Apr 20 19:24:21 2012
+
+ at author: Tillsten
+
+Changes:
+ - 13-Feb-2013 M Newville
+ complemented "report_errors" and "report_ci" with
+ "error_report" and "ci_report" (respectively) which
+ return the text of the report. Thus report_errors()
+ is simply:
+ def report_errors(params, modelpars=None, show_correl=True):
+ print error_report(params, modelpars=modelpars,
+ show_correl=show_correl)
+ and similar for report_ci() / ci_report()
+
+"""
+
+from __future__ import print_function
+from .parameter import Parameters
+import re
+
+def alphanumeric_sort(s, _nsre=re.compile('([0-9]+)')):
+ return [int(text) if text.isdigit() else text.lower()
+ for text in re.split(_nsre, s)]
+
+def getfloat_attr(obj, attr, fmt='%.3f'):
+ "format an attribute of an object for printing"
+ val = getattr(obj, attr, None)
+ if val is None:
+ return 'unknown'
+ if isinstance(val, int):
+ return '%d' % val
+ if isinstance(val, float):
+ return fmt % val
+ else:
+ return repr(val)
+
+def gformat(val, length=11):
+ """format a number with '%g'-like format, except that
+ the return will be length ``length`` (default=12)
+ and have at least length-6 significant digits
+ """
+ length = max(length, 7)
+ fmt = '{: .%ig}' % (length-6)
+ if isinstance(val, int):
+ out = ('{: .%ig}' % (length-2)).format(val)
+ if len(out) > length:
+ out = fmt.format(val)
+ else:
+ out = fmt.format(val)
+ if len(out) < length:
+ if 'e' in out:
+ ie = out.find('e')
+ if '.' not in out[:ie]:
+ out = out[:ie] + '.' + out[ie:]
+ out = out.replace('e', '0'*(length-len(out))+'e')
+ else:
+ fmt = '{: .%ig}' % (length-1)
+ out = fmt.format(val)[:length]
+ if len(out) < length:
+ pad = '0' if '.' in out else ' '
+ out += pad*(length-len(out))
+ return out
+
+CORREL_HEAD = '[[Correlations]] (unreported correlations are < % .3f)'
+
+def fit_report(inpars, modelpars=None, show_correl=True, min_correl=0.1,
+ sort_pars=False):
+ """return text of a report for fitted params best-fit values,
+ uncertainties and correlations
+
+ arguments
+ ----------
+ inpars Parameters from fit or Minizer object returned from a fit.
+ modelpars Optional Known Model Parameters [None]
+ show_correl whether to show list of sorted correlations [True]
+ min_correl smallest correlation absolute value to show [0.1]
+ sort_pars If True, then fit_report will show parameter names
+ sorted in alphanumerical order. If False, then the
+ parameters will be listed in the order they were added to
+ the Parameters dictionary. If sort_pars is callable, then
+ this (one argument) function is used to extract a
+ comparison key from each list element.
+ """
+ if isinstance(inpars, Parameters):
+ result, params = None, inpars
+ if hasattr(inpars, 'params'):
+ result = inpars
+ params = inpars.params
+
+ if sort_pars:
+ if callable(sort_pars):
+ key = sort_pars
+ else:
+ key = alphanumeric_sort
+ parnames = sorted(params, key=key)
+ else:
+ # dict.keys() returns a KeysView in py3, and they're indexed further
+ # down
+ parnames = list(params.keys())
+
+ buff = []
+ add = buff.append
+ if result is not None:
+ add("[[Fit Statistics]]")
+ add(" # function evals = %s" % getfloat_attr(result, 'nfev'))
+ add(" # data points = %s" % getfloat_attr(result, 'ndata'))
+ add(" # variables = %s" % getfloat_attr(result, 'nvarys'))
+ add(" chi-square = %s" % getfloat_attr(result, 'chisqr'))
+ add(" reduced chi-square = %s" % getfloat_attr(result, 'redchi'))
+ add(" Akaike info crit = %s" % getfloat_attr(result, 'aic'))
+ add(" Bayesian info crit = %s" % getfloat_attr(result, 'bic'))
+
+ namelen = max([len(n) for n in parnames])
+ add("[[Variables]]")
+ for name in parnames:
+ par = params[name]
+ space = ' '*(namelen+1-len(name))
+ nout = "%s:%s" % (name, space)
+ inval = '(init= ?)'
+ if par.init_value is not None:
+ inval = '(init=% .7g)' % par.init_value
+ if modelpars is not None and name in modelpars:
+ inval = '%s, model_value =% .7g' % (inval, modelpars[name].value)
+ try:
+ sval = gformat(par.value)
+ except (TypeError, ValueError):
+ sval = 'Non Numeric Value?'
+
+ if par.stderr is not None:
+ serr = gformat(par.stderr, length=9)
+
+ try:
+ spercent = '({:.2%})'.format(abs(par.stderr/par.value))
+ except ZeroDivisionError:
+ spercent = ''
+ sval = '%s +/-%s %s' % (sval, serr, spercent)
+
+ if par.vary:
+ add(" %s %s %s" % (nout, sval, inval))
+ elif par.expr is not None:
+ add(" %s %s == '%s'" % (nout, sval, par.expr))
+ else:
+ add(" %s % .7g (fixed)" % (nout, par.value))
+
+ if show_correl:
+ add(CORREL_HEAD % min_correl)
+ correls = {}
+ for i, name in enumerate(parnames):
+ par = params[name]
+ if not par.vary:
+ continue
+ if hasattr(par, 'correl') and par.correl is not None:
+ for name2 in parnames[i+1:]:
+ if (name != name2 and name2 in par.correl and
+ abs(par.correl[name2]) > min_correl):
+ correls["%s, %s" % (name, name2)] = par.correl[name2]
+
+ sort_correl = sorted(correls.items(), key=lambda it: abs(it[1]))
+ sort_correl.reverse()
+ for name, val in sort_correl:
+ lspace = max(1, 25 - len(name))
+ add(' C(%s)%s = % .3f ' % (name, (' '*30)[:lspace], val))
+ return '\n'.join(buff)
+
+
+def report_errors(params, **kws):
+ """print a report for fitted params: see error_report()"""
+ print(fit_report(params, **kws))
+
+
+def report_fit(params, **kws):
+ """print a report for fitted params: see error_report()"""
+ print(fit_report(params, **kws))
+
+
+def ci_report(ci, with_offset=True, ndigits=5):
+ """return text of a report for confidence intervals
+
+ Parameters
+ ----------
+ with_offset : bool (default `True`)
+ whether to subtract best value from all other values.
+ ndigits : int (default 5)
+ number of significant digits to show
+
+ Returns
+ -------
+ text of formatted report on confidence intervals.
+ """
+ maxlen = max([len(i) for i in ci])
+ buff = []
+ add = buff.append
+ def convp(x):
+ if abs(x[0]) < 1.e-2:
+ return "_BEST_"
+ return "%.2f%%" % (x[0]*100)
+
+ title_shown = False
+ fmt_best = fmt_diff = "{0:.%if}" % ndigits
+ if with_offset:
+ fmt_diff = "{0:+.%if}" % ndigits
+ for name, row in ci.items():
+ if not title_shown:
+ add("".join([''.rjust(maxlen+1)]+[i.rjust(ndigits+5)
+ for i in map(convp, row)]))
+ title_shown = True
+ thisrow = [" %s:" % name.ljust(maxlen)]
+ offset = 0.0
+ if with_offset:
+ for cval, val in row:
+ if abs(cval) < 1.e-2:
+ offset = val
+ for cval, val in row:
+ if cval < 1.e-2:
+ sval = fmt_best.format(val)
+ else:
+ sval = fmt_diff.format(val-offset)
+ thisrow.append(sval.rjust(ndigits+5))
+ add("".join(thisrow))
+
+ return '\n'.join(buff)
+
+
+def report_ci(ci):
+ """print a report for confidence intervals"""
+ print(ci_report(ci))
diff --git a/lmfit/ui/__init__.py b/lmfit/ui/__init__.py
index b6e3431..e835e21 100644
--- a/lmfit/ui/__init__.py
+++ b/lmfit/ui/__init__.py
@@ -1,48 +1,48 @@
-# These variables are used at the end of the module to decide
-# which BaseFitter subclass the Fitter will point to.
-import warnings
-
-has_ipython, has_matplotlib = False, False
-
-try:
- import matplotlib
-except ImportError:
- pass
-else:
- has_matplotlib = True
-
-try:
- import IPython
-except ImportError:
- warnings.warn("lmfit.Fitter will use basic mode, not IPython: need matplotlib")
-else:
- _ipy_msg1 = "lmfit.Fitter will use basic mode, not IPython: need IPython2."
- _ipy_msg2 = "lmfit.Fitter will use basic mode, not IPython: could not get IPython version"
- _ipy_msg3 = "lmfit.Fitter will use basic mode, not IPython: need ipywidgets."
- try:
- major_version = IPython.release.version_info[0]
- if major_version < 2:
- warnings.warn(_ipy_msg1)
- elif major_version > 3:
- # After IPython 3, widgets were moved to a separate package.
- # There is a shim to allow the old import, but the package has to be
- # installed for that to work.
- try:
- import ipywidgets
- except ImportError:
- warnings.warn(_ipy_msg3)
- else:
- # has_ipython = iPython installed and we are in an IPython session.
- has_ipython = IPython.get_ipython() is not None
- except Exception as e:
- warnings.warn(_ipy_msg2)
-
-from .basefitter import BaseFitter
-Fitter = BaseFitter
-if has_matplotlib:
- from .basefitter import MPLFitter
- Fitter = MPLFitter
-
-if has_ipython:
- from .ipy_fitter import NotebookFitter
- Fitter = NotebookFitter
+# These variables are used at the end of the module to decide
+# which BaseFitter subclass the Fitter will point to.
+import warnings
+
+has_ipython, has_matplotlib = False, False
+
+try:
+ import matplotlib
+except ImportError:
+ pass
+else:
+ has_matplotlib = True
+
+try:
+ import IPython
+except ImportError:
+ warnings.warn("lmfit.Fitter will use basic mode, not IPython: need matplotlib")
+else:
+ _ipy_msg1 = "lmfit.Fitter will use basic mode, not IPython: need IPython2."
+ _ipy_msg2 = "lmfit.Fitter will use basic mode, not IPython: could not get IPython version"
+ _ipy_msg3 = "lmfit.Fitter will use basic mode, not IPython: need ipywidgets."
+ try:
+ major_version = IPython.release.version_info[0]
+ if major_version < 2:
+ warnings.warn(_ipy_msg1)
+ elif major_version > 3:
+ # After IPython 3, widgets were moved to a separate package.
+ # There is a shim to allow the old import, but the package has to be
+ # installed for that to work.
+ try:
+ import ipywidgets
+ except ImportError:
+ warnings.warn(_ipy_msg3)
+ else:
+ # has_ipython = iPython installed and we are in an IPython session.
+ has_ipython = IPython.get_ipython() is not None
+ except Exception as e:
+ warnings.warn(_ipy_msg2)
+
+from .basefitter import BaseFitter
+Fitter = BaseFitter
+if has_matplotlib:
+ from .basefitter import MPLFitter
+ Fitter = MPLFitter
+
+if has_ipython:
+ from .ipy_fitter import NotebookFitter
+ Fitter = NotebookFitter
diff --git a/lmfit/ui/basefitter.py b/lmfit/ui/basefitter.py
index 8b4eace..1f8f815 100644
--- a/lmfit/ui/basefitter.py
+++ b/lmfit/ui/basefitter.py
@@ -1,320 +1,320 @@
-import warnings
-import numpy as np
-
-from ..model import Model
-from ..models import ExponentialModel # arbitrary default
-from ..asteval import Interpreter
-from ..astutils import NameFinder
-from ..parameter import check_ast_errors
-
-
-_COMMON_DOC = """
- This an interactive container for fitting models to particular data.
-
- It maintains the attributes `current_params` and `current_result`. When
- its fit() method is called, the best fit becomes the new `current_params`.
- The most basic usage is iteratively fitting data, taking advantage of
- this stateful memory that keep the parameters between each fit.
-"""
-
-_COMMON_EXAMPLES_DOC = """
-
- Examples
- --------
- >>> fitter = Fitter(data, model=SomeModel, x=x)
-
- >>> fitter.model
- # This property can be changed, to try different models on the same
- # data with the same independent vars.
- # (This is especially handy in the notebook.)
-
- >>> fitter.current_params
- # This copy of the model's Parameters is updated after each fit.
-
- >>> fitter.fit()
- # Perform a fit using fitter.current_params as a guess.
- # Optionally, pass a params argument or individual keyword arguments
- # to override current_params.
-
- >>> fitter.current_result
- # This is the result of the latest fit. It contain the usual
- # copies of the Parameters, in the attributes params and init_params.
-
- >>> fitter.data = new_data
- # If this property is updated, the `current_params` are retained an used
- # as an initial guess if fit() is called again.
- """
-
-
-class BaseFitter(object):
- __doc__ = _COMMON_DOC + """
-
- Parameters
- ----------
- data : array-like
- model : lmfit.Model
- optional initial Model to use, maybe be set or changed later
- """ + _COMMON_EXAMPLES_DOC
- def __init__(self, data, model=None, **kwargs):
- self._data = data
- self.kwargs = kwargs
-
- # GUI-based subclasses need a default value for the menu of models,
- # and so an arbitrary default is applied here, for uniformity
- # among the subclasses.
- if model is None:
- model = ExponentialModel
- self.model = model
-
- def _on_model_value_change(self, name, value):
- self.model = value
-
- def _on_fit_button_click(self, b):
- self.fit()
-
- def _on_guess_button_click(self, b):
- self.guess()
-
- @property
- def data(self):
- return self._data
-
- @data.setter
- def data(self, value):
- self._data = value
-
- @property
- def model(self):
- return self._model
-
- @model.setter
- def model(self, value):
- if callable(value):
- model = value()
- else:
- model = value
- self._model = model
- self.current_result = None
- self._current_params = model.make_params()
-
- # Use these to evaluate any Parameters that use expressions.
- self.asteval = Interpreter()
- self.namefinder = NameFinder()
-
- self._finalize_model(value)
-
- self.guess()
-
- def _finalize_model(self, value):
- # subclasses optionally override to update display here
- pass
-
- @property
- def current_params(self):
- """Each time fit() is called, these will be updated to reflect
- the latest best params. They will be used as the initial guess
- for the next fit, unless overridden by arguments to fit()."""
- return self._current_params
-
- @current_params.setter
- def current_params(self, new_params):
- # Copy contents, but retain original params objects.
- for name, par in new_params.items():
- self._current_params[name].value = par.value
- self._current_params[name].expr = par.expr
- self._current_params[name].vary = par.vary
- self._current_params[name].min = par.min
- self._current_params[name].max = par.max
-
- # Compute values for expression-based Parameters.
- self.__assign_deps(self._current_params)
- for _, par in self._current_params.items():
- if par.value is None:
- self.__update_paramval(self._current_params, par.name)
-
- self._finalize_params()
-
- def _finalize_params(self):
- # subclasses can override this to pass params to display
- pass
-
- def guess(self):
- count_indep_vars = len(self.model.independent_vars)
- guessing_successful = True
- try:
- if count_indep_vars == 0:
- guess = self.model.guess(self._data)
- elif count_indep_vars == 1:
- key = self.model.independent_vars[0]
- val = self.kwargs[key]
- d = {key: val}
- guess = self.model.guess(self._data, **d)
- except NotImplementedError:
- guessing_successful = False
- self.current_params = guess
- return guessing_successful
-
- def __assign_deps(self, params):
- # N.B. This does not use self.current_params but rather
- # new Parameters that are being built by self.guess().
- for name, par in params.items():
- if par.expr is not None:
- par.ast = self.asteval.parse(par.expr)
- check_ast_errors(self.asteval.error)
- par.deps = []
- self.namefinder.names = []
- self.namefinder.generic_visit(par.ast)
- for symname in self.namefinder.names:
- if (symname in self.current_params and
- symname not in par.deps):
- par.deps.append(symname)
- self.asteval.symtable[name] = par.value
- if par.name is None:
- par.name = name
-
- def __update_paramval(self, params, name):
- # N.B. This does not use self.current_params but rather
- # new Parameters that are being built by self.guess().
- par = params[name]
- if getattr(par, 'expr', None) is not None:
- if getattr(par, 'ast', None) is None:
- par.ast = self.asteval.parse(par.expr)
- if par.deps is not None:
- for dep in par.deps:
- self.__update_paramval(params, dep)
- par.value = self.asteval.run(par.ast)
- out = check_ast_errors(self.asteval.error)
- if out is not None:
- self.asteval.raise_exception(None)
- self.asteval.symtable[name] = par.value
-
- def fit(self, *args, **kwargs):
- "Use current_params unless overridden by arguments passed here."
- guess = dict(self.current_params)
- guess.update(self.kwargs) # from __init__, e.g. x=x
- guess.update(kwargs)
- self.current_result = self.model.fit(self._data, *args, **guess)
- self.current_params = self.current_result.params
-
-
-class MPLFitter(BaseFitter):
- # This is a small elaboration on BaseModel; it adds a plot()
- # method that depends on matplotlib. It adds several plot-
- # styling arguments to the signature.
- __doc__ = _COMMON_DOC + """
-
- Parameters
- ----------
- data : array-like
- model : lmfit.Model
- optional initial Model to use, maybe be set or changed later
-
- Additional Parameters
- ---------------------
- axes_style : dictionary representing style keyword arguments to be
- passed through to `Axes.set(...)`
- data_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the data points
- init_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the initial fit
- line
- best_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the best fit
- line
- **kwargs : independent variables or extra arguments, passed like `x=x`
- """ + _COMMON_EXAMPLES_DOC
- def __init__(self, data, model=None, axes_style={},
- data_style={}, init_style={}, best_style={}, **kwargs):
- self.axes_style = axes_style
- self.data_style = data_style
- self.init_style = init_style
- self.best_style = best_style
- super(MPLFitter, self).__init__(data, model, **kwargs)
-
- def plot(self, axes_style={}, data_style={}, init_style={}, best_style={},
- ax=None):
- """Plot data, initial guess fit, and best fit.
-
- Optional style arguments pass keyword dictionaries through to their
- respective components of the matplotlib plot.
-
- Precedence is:
- 1. arguments passed to this function, plot()
- 2. arguments passed to the Fitter when it was first declared
- 3. hard-coded defaults
-
- Parameters
- ---------------------
- axes_style : dictionary representing style keyword arguments to be
- passed through to `Axes.set(...)`
- data_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the data points
- init_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the initial fit
- line
- best_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the best fit
- line
- ax : matplotlib.Axes
- optional `Axes` object. Axes will be generated if not provided.
- """
- try:
- import matplotlib.pyplot as plt
- except ImportError:
- raise ImportError("Matplotlib is required to use this Fitter. "
- "Use BaseFitter or a subclass thereof "
- "that does not depend on matplotlib.")
-
- # Configure style
- _axes_style= dict() # none, but this is here for possible future use
- _axes_style.update(self.axes_style)
- _axes_style.update(axes_style)
- _data_style= dict(color='blue', marker='o', linestyle='none')
- _data_style.update(**_normalize_kwargs(self.data_style, 'line2d'))
- _data_style.update(**_normalize_kwargs(data_style, 'line2d'))
- _init_style = dict(color='gray')
- _init_style.update(**_normalize_kwargs(self.init_style, 'line2d'))
- _init_style.update(**_normalize_kwargs(init_style, 'line2d'))
- _best_style= dict(color='red')
- _best_style.update(**_normalize_kwargs(self.best_style, 'line2d'))
- _best_style.update(**_normalize_kwargs(best_style, 'line2d'))
-
- if ax is None:
- fig, ax = plt.subplots()
- count_indep_vars = len(self.model.independent_vars)
- if count_indep_vars == 0:
- ax.plot(self._data, **_data_style)
- elif count_indep_vars == 1:
- indep_var = self.kwargs[self.model.independent_vars[0]]
- ax.plot(indep_var, self._data, **_data_style)
- else:
- raise NotImplementedError("Cannot plot models with more than one "
- "indepedent variable.")
- result = self.current_result # alias for brevity
- if not result:
- ax.set(**_axes_style)
- return # short-circuit the rest of the plotting
- if count_indep_vars == 0:
- ax.plot(result.init_fit, **_init_style)
- ax.plot(result.best_fit, **_best_style)
- elif count_indep_vars == 1:
- ax.plot(indep_var, result.init_fit, **_init_style)
- ax.plot(indep_var, result.best_fit, **_best_style)
- ax.set(**_axes_style)
-
-
-def _normalize_kwargs(kwargs, kind='patch'):
- """Convert matplotlib keywords from short to long form."""
- # Source:
- # github.com/tritemio/FRETBursts/blob/fit_experim/fretbursts/burst_plot.py
- if kind == 'line2d':
- long_names = dict(c='color', ls='linestyle', lw='linewidth',
- mec='markeredgecolor', mew='markeredgewidth',
- mfc='markerfacecolor', ms='markersize',)
- elif kind == 'patch':
- long_names = dict(c='color', ls='linestyle', lw='linewidth',
- ec='edgecolor', fc='facecolor',)
- for short_name in long_names:
- if short_name in kwargs:
- kwargs[long_names[short_name]] = kwargs.pop(short_name)
- return kwargs
+import warnings
+import numpy as np
+
+from ..model import Model
+from ..models import ExponentialModel # arbitrary default
+from ..asteval import Interpreter
+from ..astutils import NameFinder
+from ..parameter import check_ast_errors
+
+
+_COMMON_DOC = """
+ This an interactive container for fitting models to particular data.
+
+ It maintains the attributes `current_params` and `current_result`. When
+ its fit() method is called, the best fit becomes the new `current_params`.
+ The most basic usage is iteratively fitting data, taking advantage of
+ this stateful memory that keep the parameters between each fit.
+"""
+
+_COMMON_EXAMPLES_DOC = """
+
+ Examples
+ --------
+ >>> fitter = Fitter(data, model=SomeModel, x=x)
+
+ >>> fitter.model
+ # This property can be changed, to try different models on the same
+ # data with the same independent vars.
+ # (This is especially handy in the notebook.)
+
+ >>> fitter.current_params
+ # This copy of the model's Parameters is updated after each fit.
+
+ >>> fitter.fit()
+ # Perform a fit using fitter.current_params as a guess.
+ # Optionally, pass a params argument or individual keyword arguments
+ # to override current_params.
+
+ >>> fitter.current_result
+ # This is the result of the latest fit. It contain the usual
+ # copies of the Parameters, in the attributes params and init_params.
+
+ >>> fitter.data = new_data
+ # If this property is updated, the `current_params` are retained an used
+ # as an initial guess if fit() is called again.
+ """
+
+
+class BaseFitter(object):
+ __doc__ = _COMMON_DOC + """
+
+ Parameters
+ ----------
+ data : array-like
+ model : lmfit.Model
+ optional initial Model to use, maybe be set or changed later
+ """ + _COMMON_EXAMPLES_DOC
+ def __init__(self, data, model=None, **kwargs):
+ self._data = data
+ self.kwargs = kwargs
+
+ # GUI-based subclasses need a default value for the menu of models,
+ # and so an arbitrary default is applied here, for uniformity
+ # among the subclasses.
+ if model is None:
+ model = ExponentialModel
+ self.model = model
+
+ def _on_model_value_change(self, name, value):
+ self.model = value
+
+ def _on_fit_button_click(self, b):
+ self.fit()
+
+ def _on_guess_button_click(self, b):
+ self.guess()
+
+ @property
+ def data(self):
+ return self._data
+
+ @data.setter
+ def data(self, value):
+ self._data = value
+
+ @property
+ def model(self):
+ return self._model
+
+ @model.setter
+ def model(self, value):
+ if callable(value):
+ model = value()
+ else:
+ model = value
+ self._model = model
+ self.current_result = None
+ self._current_params = model.make_params()
+
+ # Use these to evaluate any Parameters that use expressions.
+ self.asteval = Interpreter()
+ self.namefinder = NameFinder()
+
+ self._finalize_model(value)
+
+ self.guess()
+
+ def _finalize_model(self, value):
+ # subclasses optionally override to update display here
+ pass
+
+ @property
+ def current_params(self):
+ """Each time fit() is called, these will be updated to reflect
+ the latest best params. They will be used as the initial guess
+ for the next fit, unless overridden by arguments to fit()."""
+ return self._current_params
+
+ @current_params.setter
+ def current_params(self, new_params):
+ # Copy contents, but retain original params objects.
+ for name, par in new_params.items():
+ self._current_params[name].value = par.value
+ self._current_params[name].expr = par.expr
+ self._current_params[name].vary = par.vary
+ self._current_params[name].min = par.min
+ self._current_params[name].max = par.max
+
+ # Compute values for expression-based Parameters.
+ self.__assign_deps(self._current_params)
+ for _, par in self._current_params.items():
+ if par.value is None:
+ self.__update_paramval(self._current_params, par.name)
+
+ self._finalize_params()
+
+ def _finalize_params(self):
+ # subclasses can override this to pass params to display
+ pass
+
+ def guess(self):
+ count_indep_vars = len(self.model.independent_vars)
+ guessing_successful = True
+ try:
+ if count_indep_vars == 0:
+ guess = self.model.guess(self._data)
+ elif count_indep_vars == 1:
+ key = self.model.independent_vars[0]
+ val = self.kwargs[key]
+ d = {key: val}
+ guess = self.model.guess(self._data, **d)
+ except NotImplementedError:
+ guessing_successful = False
+ self.current_params = guess
+ return guessing_successful
+
+ def __assign_deps(self, params):
+ # N.B. This does not use self.current_params but rather
+ # new Parameters that are being built by self.guess().
+ for name, par in params.items():
+ if par.expr is not None:
+ par.ast = self.asteval.parse(par.expr)
+ check_ast_errors(self.asteval.error)
+ par.deps = []
+ self.namefinder.names = []
+ self.namefinder.generic_visit(par.ast)
+ for symname in self.namefinder.names:
+ if (symname in self.current_params and
+ symname not in par.deps):
+ par.deps.append(symname)
+ self.asteval.symtable[name] = par.value
+ if par.name is None:
+ par.name = name
+
+ def __update_paramval(self, params, name):
+ # N.B. This does not use self.current_params but rather
+ # new Parameters that are being built by self.guess().
+ par = params[name]
+ if getattr(par, 'expr', None) is not None:
+ if getattr(par, 'ast', None) is None:
+ par.ast = self.asteval.parse(par.expr)
+ if par.deps is not None:
+ for dep in par.deps:
+ self.__update_paramval(params, dep)
+ par.value = self.asteval.run(par.ast)
+ out = check_ast_errors(self.asteval.error)
+ if out is not None:
+ self.asteval.raise_exception(None)
+ self.asteval.symtable[name] = par.value
+
+ def fit(self, *args, **kwargs):
+ "Use current_params unless overridden by arguments passed here."
+ guess = dict(self.current_params)
+ guess.update(self.kwargs) # from __init__, e.g. x=x
+ guess.update(kwargs)
+ self.current_result = self.model.fit(self._data, *args, **guess)
+ self.current_params = self.current_result.params
+
+
+class MPLFitter(BaseFitter):
+ # This is a small elaboration on BaseModel; it adds a plot()
+ # method that depends on matplotlib. It adds several plot-
+ # styling arguments to the signature.
+ __doc__ = _COMMON_DOC + """
+
+ Parameters
+ ----------
+ data : array-like
+ model : lmfit.Model
+ optional initial Model to use, maybe be set or changed later
+
+ Additional Parameters
+ ---------------------
+ axes_style : dictionary representing style keyword arguments to be
+ passed through to `Axes.set(...)`
+ data_style : dictionary representing style keyword arguments to be passed
+ through to the matplotlib `plot()` command the plots the data points
+ init_style : dictionary representing style keyword arguments to be passed
+ through to the matplotlib `plot()` command the plots the initial fit
+ line
+ best_style : dictionary representing style keyword arguments to be passed
+ through to the matplotlib `plot()` command the plots the best fit
+ line
+ **kwargs : independent variables or extra arguments, passed like `x=x`
+ """ + _COMMON_EXAMPLES_DOC
+ def __init__(self, data, model=None, axes_style={},
+ data_style={}, init_style={}, best_style={}, **kwargs):
+ self.axes_style = axes_style
+ self.data_style = data_style
+ self.init_style = init_style
+ self.best_style = best_style
+ super(MPLFitter, self).__init__(data, model, **kwargs)
+
+ def plot(self, axes_style={}, data_style={}, init_style={}, best_style={},
+ ax=None):
+ """Plot data, initial guess fit, and best fit.
+
+ Optional style arguments pass keyword dictionaries through to their
+ respective components of the matplotlib plot.
+
+ Precedence is:
+ 1. arguments passed to this function, plot()
+ 2. arguments passed to the Fitter when it was first declared
+ 3. hard-coded defaults
+
+ Parameters
+ ---------------------
+ axes_style : dictionary representing style keyword arguments to be
+ passed through to `Axes.set(...)`
+ data_style : dictionary representing style keyword arguments to be passed
+ through to the matplotlib `plot()` command the plots the data points
+ init_style : dictionary representing style keyword arguments to be passed
+ through to the matplotlib `plot()` command the plots the initial fit
+ line
+ best_style : dictionary representing style keyword arguments to be passed
+ through to the matplotlib `plot()` command the plots the best fit
+ line
+ ax : matplotlib.Axes
+ optional `Axes` object. Axes will be generated if not provided.
+ """
+ try:
+ import matplotlib.pyplot as plt
+ except ImportError:
+ raise ImportError("Matplotlib is required to use this Fitter. "
+ "Use BaseFitter or a subclass thereof "
+ "that does not depend on matplotlib.")
+
+ # Configure style
+ _axes_style= dict() # none, but this is here for possible future use
+ _axes_style.update(self.axes_style)
+ _axes_style.update(axes_style)
+ _data_style= dict(color='blue', marker='o', linestyle='none')
+ _data_style.update(**_normalize_kwargs(self.data_style, 'line2d'))
+ _data_style.update(**_normalize_kwargs(data_style, 'line2d'))
+ _init_style = dict(color='gray')
+ _init_style.update(**_normalize_kwargs(self.init_style, 'line2d'))
+ _init_style.update(**_normalize_kwargs(init_style, 'line2d'))
+ _best_style= dict(color='red')
+ _best_style.update(**_normalize_kwargs(self.best_style, 'line2d'))
+ _best_style.update(**_normalize_kwargs(best_style, 'line2d'))
+
+ if ax is None:
+ fig, ax = plt.subplots()
+ count_indep_vars = len(self.model.independent_vars)
+ if count_indep_vars == 0:
+ ax.plot(self._data, **_data_style)
+ elif count_indep_vars == 1:
+ indep_var = self.kwargs[self.model.independent_vars[0]]
+ ax.plot(indep_var, self._data, **_data_style)
+ else:
+ raise NotImplementedError("Cannot plot models with more than one "
+ "indepedent variable.")
+ result = self.current_result # alias for brevity
+ if not result:
+ ax.set(**_axes_style)
+ return # short-circuit the rest of the plotting
+ if count_indep_vars == 0:
+ ax.plot(result.init_fit, **_init_style)
+ ax.plot(result.best_fit, **_best_style)
+ elif count_indep_vars == 1:
+ ax.plot(indep_var, result.init_fit, **_init_style)
+ ax.plot(indep_var, result.best_fit, **_best_style)
+ ax.set(**_axes_style)
+
+
+def _normalize_kwargs(kwargs, kind='patch'):
+ """Convert matplotlib keywords from short to long form."""
+ # Source:
+ # github.com/tritemio/FRETBursts/blob/fit_experim/fretbursts/burst_plot.py
+ if kind == 'line2d':
+ long_names = dict(c='color', ls='linestyle', lw='linewidth',
+ mec='markeredgecolor', mew='markeredgewidth',
+ mfc='markerfacecolor', ms='markersize',)
+ elif kind == 'patch':
+ long_names = dict(c='color', ls='linestyle', lw='linewidth',
+ ec='edgecolor', fc='facecolor',)
+ for short_name in long_names:
+ if short_name in kwargs:
+ kwargs[long_names[short_name]] = kwargs.pop(short_name)
+ return kwargs
diff --git a/lmfit/ui/ipy_fitter.py b/lmfit/ui/ipy_fitter.py
index 29c9446..80edda5 100644
--- a/lmfit/ui/ipy_fitter.py
+++ b/lmfit/ui/ipy_fitter.py
@@ -1,282 +1,282 @@
-import warnings
-import numpy as np
-
-from ..model import Model
-
-from .basefitter import MPLFitter, _COMMON_DOC, _COMMON_EXAMPLES_DOC
-
-# Note: If IPython is not available of the version is < 2,
-# this module will not be imported, and a different Fitter.
-
-import IPython
-from IPython.display import display, clear_output
-# Widgets were only experimental in IPython 2.x, but this does work there.
-# Handle the change in naming from 2.x to 3.x.
-IPY2 = IPython.release.version_info[0] == 2
-IPY3 = IPython.release.version_info[0] == 3
-if IPY2:
- from IPython.html.widgets import DropdownWidget as Dropdown
- from IPython.html.widgets import ButtonWidget as Button
- from IPython.html.widgets import ContainerWidget
- from IPython.html.widgets import FloatTextWidget as FloatText
- from IPython.html.widgets import CheckboxWidget as Checkbox
- class HBox(ContainerWidget):
- def __init__(self, *args, **kwargs):
- self.add_class('hbox')
- super(self, ContainerWidget).__init__(*args, **kwargs)
-elif IPY3:
- # as of IPython 3.x:
- from IPython.html.widgets import Dropdown
- from IPython.html.widgets import Button
- from IPython.html.widgets import HBox
- from IPython.html.widgets import FloatText
- from IPython.html.widgets import Checkbox
-else:
- # as of IPython 4.x+:
- from ipywidgets import Dropdown
- from ipywidgets import Button
- from ipywidgets import HBox
- from ipywidgets import FloatText
- from ipywidgets import Checkbox
-
-
-class ParameterWidgetGroup(object):
- """Construct several widgets that together represent a Parameter.
-
- This will only be used if IPython is available."""
- def __init__(self, par):
- self.par = par
-
- # Define widgets.
- self.value_text = FloatText(description=par.name,
- min=self.par.min, max=self.par.max)
- self.value_text.width = 100
- self.min_text = FloatText(description='min', max=self.par.max)
- self.min_text.width = 100
- self.max_text = FloatText(description='max', min=self.par.min)
- self.max_text.width = 100
- self.min_checkbox = Checkbox(description='min')
- self.max_checkbox = Checkbox(description='max')
- self.vary_checkbox = Checkbox(description='vary')
-
- # Set widget values and visibility.
- if par.value is not None:
- self.value_text.value = self.par.value
- min_unset = self.par.min is None or self.par.min == -np.inf
- max_unset = self.par.max is None or self.par.max == np.inf
- self.min_checkbox.value = not min_unset
- self.min_text.visible = not min_unset
- self.min_text.value = self.par.min
- self.max_checkbox.value = not max_unset
- self.max_text.visible = not max_unset
- self.max_text.value = self.par.max
- self.vary_checkbox.value = self.par.vary
-
- # Configure widgets to sync with par attributes.
- self.value_text.on_trait_change(self._on_value_change, 'value')
- self.min_text.on_trait_change(self._on_min_value_change, 'value')
- self.max_text.on_trait_change(self._on_max_value_change, 'value')
- self.min_checkbox.on_trait_change(self._on_min_checkbox_change,
- 'value')
- self.max_checkbox.on_trait_change(self._on_max_checkbox_change,
- 'value')
- self.vary_checkbox.on_trait_change(self._on_vary_change, 'value')
-
- def _on_value_change(self, name, value):
- self.par.value = value
-
- def _on_min_checkbox_change(self, name, value):
- self.min_text.visible = value
- if value:
- # -np.inf does not play well with a numerical text field,
- # so set min to -1 if activated (and back to -inf if deactivated).
- self.min_text.value = -1
- self.par.min = self.min_text.value
- self.value_text.min = self.min_text.value
- else:
- self.par.min = None
-
- def _on_max_checkbox_change(self, name, value):
- self.max_text.visible = value
- if value:
- # np.inf does not play well with a numerical text field,
- # so set max to 1 if activated (and back to inf if deactivated).
- self.max_text.value = 1
- self.par.max = self.max_text.value
- self.value_text.max = self.max_text.value
- else:
- self.par.max = None
-
- def _on_min_value_change(self, name, value):
- self.par.min = value
- self.value_text.min = value
- self.max_text.min = value
-
- def _on_max_value_change(self, name, value):
- self.par.max = value
- self.value_text.max = value
- self.min_text.max = value
-
- def _on_vary_change(self, name, value):
- self.par.vary = value
- # self.value_text.disabled = not value
-
- def close(self):
- # one convenience method to close (i.e., hide and disconnect) all
- # widgets in this group
- self.value_text.close()
- self.min_text.close()
- self.max_text.close()
- self.vary_checkbox.close()
- self.min_checkbox.close()
- self.max_checkbox.close()
-
- def _repr_html_(self):
- box = HBox()
- box.children = [self.value_text, self.vary_checkbox,
- self.min_checkbox, self.min_text,
- self.max_checkbox, self.max_text]
- display(box)
-
- # Make it easy to set the widget attributes directly.
- @property
- def value(self):
- return self.value_text.value
-
- @value.setter
- def value(self, value):
- self.value_text.value = value
-
- @property
- def vary(self):
- return self.vary_checkbox.value
-
- @vary.setter
- def vary(self, value):
- self.vary_checkbox.value = value
-
- @property
- def min(self):
- return self.min_text.value
-
- @min.setter
- def min(self, value):
- self.min_text.value = value
-
- @property
- def max(self):
- return self.max_text.value
-
- @max.setter
- def max(self, value):
- self.max_text.value = value
-
- @property
- def name(self):
- return self.par.name
-
-
-class NotebookFitter(MPLFitter):
- __doc__ = _COMMON_DOC + """
- If IPython is available, it uses the IPython notebook's rich display
- to fit data interactively in a web-based GUI. The Parameters are
- represented in a web-based form that is kept in sync with `current_params`.
- All subclasses to Model, including user-defined ones, are shown in a
- drop-down menu.
-
- Clicking the "Fit" button updates a plot, as above, and updates the
- Parameters in the form to reflect the best fit.
-
- Parameters
- ----------
- data : array-like
- model : lmfit.Model
- optional initial Model to use, maybe be set or changed later
- all_models : list
- optional list of Models to populate drop-down menu, by default
- all built-in and user-defined subclasses of Model are used
-
- Additional Parameters
- ---------------------
- axes_style : dictionary representing style keyword arguments to be
- passed through to `Axes.set(...)`
- data_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the data points
- init_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the initial fit
- line
- best_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the best fit
- line
- **kwargs : independent variables or extra arguments, passed like `x=x`
- """ + _COMMON_EXAMPLES_DOC
- def __init__(self, data, model=None, all_models=None, axes_style={},
- data_style={}, init_style={}, best_style={}, **kwargs):
- # Dropdown menu of all subclasses of Model, incl. user-defined.
- self.models_menu = Dropdown()
- # Dropbox API is very different between IPy 2.x and 3.x.
- if IPY2:
- if all_models is None:
- all_models = dict([(m.__name__, m) for m in Model.__subclasses__()])
- self.models_menu.values = all_models
- else:
- if all_models is None:
- all_models = [(m.__name__, m) for m in Model.__subclasses__()]
- self.models_menu.options = all_models
- self.models_menu.on_trait_change(self._on_model_value_change,
- 'value')
- # Button to trigger fitting.
- self.fit_button = Button(description='Fit')
- self.fit_button.on_click(self._on_fit_button_click)
-
- # Button to trigger guessing.
- self.guess_button = Button(description='Auto-Guess')
- self.guess_button.on_click(self._on_guess_button_click)
-
- # Parameter widgets are not built here. They are (re-)built when
- # the model is (re-)set.
- super(NotebookFitter, self).__init__(data, model, axes_style,
- data_style, init_style,
- best_style, **kwargs)
-
- def _repr_html_(self):
- display(self.models_menu)
- button_box = HBox()
- button_box.children = [self.fit_button, self.guess_button]
- display(button_box)
- for pw in self.param_widgets:
- display(pw)
- self.plot()
-
- def guess(self):
- guessing_successful = super(NotebookFitter, self).guess()
- self.guess_button.disabled = not guessing_successful
-
- def _finalize_model(self, value):
- first_run = not hasattr(self, 'param_widgets')
- if not first_run:
- # Remove all Parameter widgets, and replace them with widgets
- # for the new model.
- for pw in self.param_widgets:
- pw.close()
- self.models_menu.value = value
- self.param_widgets = [ParameterWidgetGroup(p)
- for _, p in self._current_params.items()]
- if not first_run:
- for pw in self.param_widgets:
- display(pw)
-
- def _finalize_params(self):
- for pw in self.param_widgets:
- pw.value = self._current_params[pw.name].value
- pw.min = self._current_params[pw.name].min
- pw.max = self._current_params[pw.name].max
- pw.vary = self._current_params[pw.name].vary
-
- def plot(self):
- clear_output(wait=True)
- super(NotebookFitter, self).plot()
-
- def fit(self):
- super(NotebookFitter, self).fit()
- self.plot()
+import warnings
+import numpy as np
+
+from ..model import Model
+
+from .basefitter import MPLFitter, _COMMON_DOC, _COMMON_EXAMPLES_DOC
+
+# Note: If IPython is not available of the version is < 2,
+# this module will not be imported, and a different Fitter.
+
+import IPython
+from IPython.display import display, clear_output
+# Widgets were only experimental in IPython 2.x, but this does work there.
+# Handle the change in naming from 2.x to 3.x.
+IPY2 = IPython.release.version_info[0] == 2
+IPY3 = IPython.release.version_info[0] == 3
+if IPY2:
+ from IPython.html.widgets import DropdownWidget as Dropdown
+ from IPython.html.widgets import ButtonWidget as Button
+ from IPython.html.widgets import ContainerWidget
+ from IPython.html.widgets import FloatTextWidget as FloatText
+ from IPython.html.widgets import CheckboxWidget as Checkbox
+ class HBox(ContainerWidget):
+ def __init__(self, *args, **kwargs):
+ self.add_class('hbox')
+ super(self, ContainerWidget).__init__(*args, **kwargs)
+elif IPY3:
+ # as of IPython 3.x:
+ from IPython.html.widgets import Dropdown
+ from IPython.html.widgets import Button
+ from IPython.html.widgets import HBox
+ from IPython.html.widgets import FloatText
+ from IPython.html.widgets import Checkbox
+else:
+ # as of IPython 4.x+:
+ from ipywidgets import Dropdown
+ from ipywidgets import Button
+ from ipywidgets import HBox
+ from ipywidgets import FloatText
+ from ipywidgets import Checkbox
+
+
+class ParameterWidgetGroup(object):
+ """Construct several widgets that together represent a Parameter.
+
+ This will only be used if IPython is available."""
+ def __init__(self, par):
+ self.par = par
+
+ # Define widgets.
+ self.value_text = FloatText(description=par.name,
+ min=self.par.min, max=self.par.max)
+ self.value_text.width = 100
+ self.min_text = FloatText(description='min', max=self.par.max)
+ self.min_text.width = 100
+ self.max_text = FloatText(description='max', min=self.par.min)
+ self.max_text.width = 100
+ self.min_checkbox = Checkbox(description='min')
+ self.max_checkbox = Checkbox(description='max')
+ self.vary_checkbox = Checkbox(description='vary')
+
+ # Set widget values and visibility.
+ if par.value is not None:
+ self.value_text.value = self.par.value
+ min_unset = self.par.min is None or self.par.min == -np.inf
+ max_unset = self.par.max is None or self.par.max == np.inf
+ self.min_checkbox.value = not min_unset
+ self.min_text.visible = not min_unset
+ self.min_text.value = self.par.min
+ self.max_checkbox.value = not max_unset
+ self.max_text.visible = not max_unset
+ self.max_text.value = self.par.max
+ self.vary_checkbox.value = self.par.vary
+
+ # Configure widgets to sync with par attributes.
+ self.value_text.on_trait_change(self._on_value_change, 'value')
+ self.min_text.on_trait_change(self._on_min_value_change, 'value')
+ self.max_text.on_trait_change(self._on_max_value_change, 'value')
+ self.min_checkbox.on_trait_change(self._on_min_checkbox_change,
+ 'value')
+ self.max_checkbox.on_trait_change(self._on_max_checkbox_change,
+ 'value')
+ self.vary_checkbox.on_trait_change(self._on_vary_change, 'value')
+
+ def _on_value_change(self, name, value):
+ self.par.value = value
+
+ def _on_min_checkbox_change(self, name, value):
+ self.min_text.visible = value
+ if value:
+ # -np.inf does not play well with a numerical text field,
+ # so set min to -1 if activated (and back to -inf if deactivated).
+ self.min_text.value = -1
+ self.par.min = self.min_text.value
+ self.value_text.min = self.min_text.value
+ else:
+ self.par.min = None
+
+ def _on_max_checkbox_change(self, name, value):
+ self.max_text.visible = value
+ if value:
+ # np.inf does not play well with a numerical text field,
+ # so set max to 1 if activated (and back to inf if deactivated).
+ self.max_text.value = 1
+ self.par.max = self.max_text.value
+ self.value_text.max = self.max_text.value
+ else:
+ self.par.max = None
+
+ def _on_min_value_change(self, name, value):
+ self.par.min = value
+ self.value_text.min = value
+ self.max_text.min = value
+
+ def _on_max_value_change(self, name, value):
+ self.par.max = value
+ self.value_text.max = value
+ self.min_text.max = value
+
+ def _on_vary_change(self, name, value):
+ self.par.vary = value
+ # self.value_text.disabled = not value
+
+ def close(self):
+ # one convenience method to close (i.e., hide and disconnect) all
+ # widgets in this group
+ self.value_text.close()
+ self.min_text.close()
+ self.max_text.close()
+ self.vary_checkbox.close()
+ self.min_checkbox.close()
+ self.max_checkbox.close()
+
+ def _repr_html_(self):
+ box = HBox()
+ box.children = [self.value_text, self.vary_checkbox,
+ self.min_checkbox, self.min_text,
+ self.max_checkbox, self.max_text]
+ display(box)
+
+ # Make it easy to set the widget attributes directly.
+ @property
+ def value(self):
+ return self.value_text.value
+
+ @value.setter
+ def value(self, value):
+ self.value_text.value = value
+
+ @property
+ def vary(self):
+ return self.vary_checkbox.value
+
+ @vary.setter
+ def vary(self, value):
+ self.vary_checkbox.value = value
+
+ @property
+ def min(self):
+ return self.min_text.value
+
+ @min.setter
+ def min(self, value):
+ self.min_text.value = value
+
+ @property
+ def max(self):
+ return self.max_text.value
+
+ @max.setter
+ def max(self, value):
+ self.max_text.value = value
+
+ @property
+ def name(self):
+ return self.par.name
+
+
+class NotebookFitter(MPLFitter):
+ __doc__ = _COMMON_DOC + """
+ If IPython is available, it uses the IPython notebook's rich display
+ to fit data interactively in a web-based GUI. The Parameters are
+ represented in a web-based form that is kept in sync with `current_params`.
+ All subclasses to Model, including user-defined ones, are shown in a
+ drop-down menu.
+
+ Clicking the "Fit" button updates a plot, as above, and updates the
+ Parameters in the form to reflect the best fit.
+
+ Parameters
+ ----------
+ data : array-like
+ model : lmfit.Model
+ optional initial Model to use, maybe be set or changed later
+ all_models : list
+ optional list of Models to populate drop-down menu, by default
+ all built-in and user-defined subclasses of Model are used
+
+ Additional Parameters
+ ---------------------
+ axes_style : dictionary representing style keyword arguments to be
+ passed through to `Axes.set(...)`
+ data_style : dictionary representing style keyword arguments to be passed
+ through to the matplotlib `plot()` command the plots the data points
+ init_style : dictionary representing style keyword arguments to be passed
+ through to the matplotlib `plot()` command the plots the initial fit
+ line
+ best_style : dictionary representing style keyword arguments to be passed
+ through to the matplotlib `plot()` command the plots the best fit
+ line
+ **kwargs : independent variables or extra arguments, passed like `x=x`
+ """ + _COMMON_EXAMPLES_DOC
+ def __init__(self, data, model=None, all_models=None, axes_style={},
+ data_style={}, init_style={}, best_style={}, **kwargs):
+ # Dropdown menu of all subclasses of Model, incl. user-defined.
+ self.models_menu = Dropdown()
+ # Dropbox API is very different between IPy 2.x and 3.x.
+ if IPY2:
+ if all_models is None:
+ all_models = dict([(m.__name__, m) for m in Model.__subclasses__()])
+ self.models_menu.values = all_models
+ else:
+ if all_models is None:
+ all_models = [(m.__name__, m) for m in Model.__subclasses__()]
+ self.models_menu.options = all_models
+ self.models_menu.on_trait_change(self._on_model_value_change,
+ 'value')
+ # Button to trigger fitting.
+ self.fit_button = Button(description='Fit')
+ self.fit_button.on_click(self._on_fit_button_click)
+
+ # Button to trigger guessing.
+ self.guess_button = Button(description='Auto-Guess')
+ self.guess_button.on_click(self._on_guess_button_click)
+
+ # Parameter widgets are not built here. They are (re-)built when
+ # the model is (re-)set.
+ super(NotebookFitter, self).__init__(data, model, axes_style,
+ data_style, init_style,
+ best_style, **kwargs)
+
+ def _repr_html_(self):
+ display(self.models_menu)
+ button_box = HBox()
+ button_box.children = [self.fit_button, self.guess_button]
+ display(button_box)
+ for pw in self.param_widgets:
+ display(pw)
+ self.plot()
+
+ def guess(self):
+ guessing_successful = super(NotebookFitter, self).guess()
+ self.guess_button.disabled = not guessing_successful
+
+ def _finalize_model(self, value):
+ first_run = not hasattr(self, 'param_widgets')
+ if not first_run:
+ # Remove all Parameter widgets, and replace them with widgets
+ # for the new model.
+ for pw in self.param_widgets:
+ pw.close()
+ self.models_menu.value = value
+ self.param_widgets = [ParameterWidgetGroup(p)
+ for _, p in self._current_params.items()]
+ if not first_run:
+ for pw in self.param_widgets:
+ display(pw)
+
+ def _finalize_params(self):
+ for pw in self.param_widgets:
+ pw.value = self._current_params[pw.name].value
+ pw.min = self._current_params[pw.name].min
+ pw.max = self._current_params[pw.name].max
+ pw.vary = self._current_params[pw.name].vary
+
+ def plot(self):
+ clear_output(wait=True)
+ super(NotebookFitter, self).plot()
+
+ def fit(self):
+ super(NotebookFitter, self).fit()
+ self.plot()
diff --git a/lmfit/uncertainties/__init__.py b/lmfit/uncertainties/__init__.py
index 829a283..5c2ec34 100644
--- a/lmfit/uncertainties/__init__.py
+++ b/lmfit/uncertainties/__init__.py
@@ -1,1645 +1,1645 @@
-#!! Whenever the documentation below is updated, setup.py should be
-# checked for consistency.
-
-'''
-Calculations with full error propagation for quantities with uncertainties.
-Derivatives can also be calculated.
-
-Web user guide: http://packages.python.org/uncertainties/.
-
-Example of possible calculation: (0.2 +/- 0.01)**2 = 0.04 +/- 0.004.
-
-Correlations between expressions are correctly taken into account (for
-instance, with x = 0.2+/-0.01, 2*x-x-x is exactly zero, as is y-x-x
-with y = 2*x).
-
-Examples:
-
- import uncertainties
- from uncertainties import ufloat
- from uncertainties.umath import * # sin(), etc.
-
- # Mathematical operations:
- x = ufloat((0.20, 0.01)) # x = 0.20+/-0.01
- x = ufloat("0.20+/-0.01") # Other representation
- x = ufloat("0.20(1)") # Other representation
- x = ufloat("0.20") # Implicit uncertainty of +/-1 on the last digit
- print x**2 # Square: prints "0.04+/-0.004"
- print sin(x**2) # Prints "0.0399...+/-0.00399..."
-
- print x.std_score(0.17) # Prints "-3.0": deviation of -3 sigmas
-
- # Access to the nominal value, and to the uncertainty:
- square = x**2 # Square
- print square # Prints "0.04+/-0.004"
- print square.nominal_value # Prints "0.04"
- print square.std_dev() # Prints "0.004..."
-
- print square.derivatives[x] # Partial derivative: 0.4 (= 2*0.20)
-
- # Correlations:
- u = ufloat((1, 0.05), "u variable") # Tag
- v = ufloat((10, 0.1), "v variable")
- sum_value = u+v
-
- u.set_std_dev(0.1) # Standard deviations can be updated on the fly
- print sum_value - u - v # Prints "0.0" (exact result)
-
- # List of all sources of error:
- print sum_value # Prints "11+/-0.1414..."
- for (var, error) in sum_value.error_components().items():
- print "%s: %f" % (var.tag, error) # Individual error components
-
- # Covariance matrices:
- cov_matrix = uncertainties.covariance_matrix([u, v, sum_value])
- print cov_matrix # 3x3 matrix
-
- # Correlated variables can be constructed from a covariance matrix, if
- # NumPy is available:
- (u2, v2, sum2) = uncertainties.correlated_values([1, 10, 11],
- cov_matrix)
- print u2 # Value and uncertainty of u: correctly recovered (1+/-0.1)
- print uncertainties.covariance_matrix([u2, v2, sum2]) # == cov_matrix
-
-- The main function provided by this module is ufloat, which creates
-numbers with uncertainties (Variable objects). Variable objects can
-be used as if they were regular Python numbers. The main attributes
-and methods of Variable objects are defined in the documentation of
-the Variable class.
-
-- Valid operations on numbers with uncertainties include basic
-mathematical functions (addition, etc.).
-
-Most operations from the standard math module (sin, etc.) can be applied
-on numbers with uncertainties by using their generalization from the
-uncertainties.umath module:
-
- from uncertainties.umath import sin
- print sin(ufloat("1+/-0.01")) # 0.841...+/-0.005...
- print sin(1) # umath.sin() also works on floats, exactly like math.sin()
-
-Logical operations (>, ==, etc.) are also supported.
-
-Basic operations on NumPy arrays or matrices of numbers with
-uncertainties can be performed:
-
- 2*numpy.array([ufloat((1, 0.01)), ufloat((2, 0.1))])
-
-More complex operations on NumPy arrays can be performed through the
-dedicated uncertainties.unumpy sub-module (see its documentation).
-
-Calculations that are performed through non-Python code (Fortran, C,
-etc.) can handle numbers with uncertainties instead of floats through
-the provided wrap() wrapper:
-
- import uncertainties
-
- # wrapped_f is a version of f that can take arguments with
- # uncertainties, even if f only takes floats:
- wrapped_f = uncertainties.wrap(f)
-
-If some derivatives of the wrapped function f are known (analytically,
-or numerically), they can be given to wrap()--see the documentation
-for wrap().
-
-- Utility functions are also provided: the covariance matrix between
-random variables can be calculated with covariance_matrix(), or used
-as input for the definition of correlated quantities (correlated_values()
-function--defined only if the NumPy module is available).
-
-- Mathematical expressions involving numbers with uncertainties
-generally return AffineScalarFunc objects, which also print as a value
-with uncertainty. Their most useful attributes and methods are
-described in the documentation for AffineScalarFunc. Note that
-Variable objects are also AffineScalarFunc objects. UFloat is an
-alias for AffineScalarFunc, provided as a convenience: testing whether
-a value carries an uncertainty handled by this module should be done
-with insinstance(my_value, UFloat).
-
-- Mathematically, numbers with uncertainties are, in this package,
-probability distributions. These probabilities are reduced to two
-numbers: a nominal value and an uncertainty. Thus, both variables
-(Variable objects) and the result of mathematical operations
-(AffineScalarFunc objects) contain these two values (respectively in
-their nominal_value attribute and through their std_dev() method).
-
-The uncertainty of a number with uncertainty is simply defined in
-this package as the standard deviation of the underlying probability
-distribution.
-
-The numbers with uncertainties manipulated by this package are assumed
-to have a probability distribution mostly contained around their
-nominal value, in an interval of about the size of their standard
-deviation. This should cover most practical cases. A good choice of
-nominal value for a number with uncertainty is thus the median of its
-probability distribution, the location of highest probability, or the
-average value.
-
-- When manipulating ensembles of numbers, some of which contain
-uncertainties, it can be useful to access the nominal value and
-uncertainty of all numbers in a uniform manner:
-
- x = ufloat("3+/-0.1")
- print nominal_value(x) # Prints 3
- print std_dev(x) # Prints 0.1
- print nominal_value(3) # Prints 3: nominal_value works on floats
- print std_dev(3) # Prints 0: std_dev works on floats
-
-- Probability distributions (random variables and calculation results)
-are printed as:
-
- nominal value +/- standard deviation
-
-but this does not imply any property on the nominal value (beyond the
-fact that the nominal value is normally inside the region of high
-probability density), or that the probability distribution of the
-result is symmetrical (this is rarely strictly the case).
-
-- Linear approximations of functions (around the nominal values) are
-used for the calculation of the standard deviation of mathematical
-expressions with this package.
-
-The calculated standard deviations and nominal values are thus
-meaningful approximations as long as the functions involved have
-precise linear expansions in the region where the probability
-distribution of their variables is the largest. It is therefore
-important that uncertainties be small. Mathematically, this means
-that the linear term of functions around the nominal values of their
-variables should be much larger than the remaining higher-order terms
-over the region of significant probability.
-
-For instance, sin(0+/-0.01) yields a meaningful standard deviation
-since it is quite linear over 0+/-0.01. However, cos(0+/-0.01) yields
-an approximate standard deviation of 0 (because the cosine is not well
-approximated by a line around 0), which might not be precise enough
-for all applications.
-
-- Comparison operations (>, ==, etc.) on numbers with uncertainties
-have a pragmatic semantics, in this package: numbers with
-uncertainties can be used wherever Python numbers are used, most of
-the time with a result identical to the one that would be obtained
-with their nominal value only. However, since the objects defined in
-this module represent probability distributions and not pure numbers,
-comparison operator are interpreted in a specific way.
-
-The result of a comparison operation ("==", ">", etc.) is defined so as
-to be essentially consistent with the requirement that uncertainties
-be small: the value of a comparison operation is True only if the
-operation yields True for all infinitesimal variations of its random
-variables, except, possibly, for an infinitely small number of cases.
-
-Example:
-
- "x = 3.14; y = 3.14" is such that x == y
-
-but
-
- x = ufloat((3.14, 0.01))
- y = ufloat((3.14, 0.01))
-
-is not such that x == y, since x and y are independent random
-variables that almost never give the same value. However, x == x
-still holds.
-
-The boolean value (bool(x), "if x...") of a number with uncertainty x
-is the result of x != 0.
-
-- The uncertainties package is for Python 2.5 and above.
-
-- This package contains tests. They can be run either manually or
-automatically with the nose unit testing framework (nosetests).
-
-(c) 2009-2013 by Eric O. LEBIGOT (EOL) <eric.lebigot at normalesup.org>.
-Please send feature requests, bug reports, or feedback to this address.
-
-Please support future development by donating $5 or more through PayPal!
-
-This software is released under a dual license. (1) The BSD license.
-(2) Any other license, as long as it is obtained from the original
-author.'''
-
-# The idea behind this module is to replace the result of mathematical
-# operations by a local approximation of the defining function. For
-# example, sin(0.2+/-0.01) becomes the affine function
-# (AffineScalarFunc object) whose nominal value is sin(0.2) and
-# whose variations are given by sin(0.2+delta) = 0.98...*delta.
-# Uncertainties can then be calculated by using this local linear
-# approximation of the original function.
-
-from __future__ import division # Many analytical derivatives depend on this
-
-import re
-import math
-from math import sqrt, log # Optimization: no attribute look-up
-import copy
-import warnings
-
-# Numerical version:
-__version_info__ = (1, 9)
-__version__ = '.'.join(map(str, __version_info__))
-
-__author__ = 'Eric O. LEBIGOT (EOL) <eric.lebigot at normalesup.org>'
-
-# Attributes that are always exported (some other attributes are
-# exported only if the NumPy module is available...):
-__all__ = [
-
- # All sub-modules and packages are not imported by default,
- # in particular because NumPy might be unavailable.
- 'ufloat', # Main function: returns a number with uncertainty
-
- # Uniform access to nominal values and standard deviations:
- 'nominal_value',
- 'std_dev',
-
- # Utility functions (more are exported if NumPy is present):
- 'covariance_matrix',
-
- # Class for testing whether an object is a number with
- # uncertainty. Not usually created by users (except through the
- # Variable subclass), but possibly manipulated by external code
- # ['derivatives()' method, etc.].
- 'UFloat',
-
- # Wrapper for allowing non-pure-Python function to handle
- # quantities with uncertainties:
- 'wrap',
-
- # The documentation for wrap() indicates that numerical
- # derivatives are calculated through partial_derivative(). The
- # user might also want to change the size of the numerical
- # differentiation step.
- 'partial_derivative'
- ]
-
-###############################################################################
-
-def set_doc(doc_string):
- """
- Decorator function that sets the docstring to the given text.
-
- It is useful for functions whose docstring is calculated
- (including string substitutions).
- """
- def set_doc_string(func):
- func.__doc__ = doc_string
- return func
- return set_doc_string
-
-# Some types known to not depend on Variable objects are put in
-# CONSTANT_TYPES. The most common types can be put in front, as this
-# may slightly improve the execution speed.
-CONSTANT_TYPES = (float, int, complex) # , long)
-
-###############################################################################
-# Utility for issuing deprecation warnings
-
-def deprecation(message):
- '''
- Warns the user with the given message, by issuing a
- DeprecationWarning.
- '''
- warnings.warn(message, DeprecationWarning, stacklevel=2)
-
-
-###############################################################################
-
-## Definitions that depend on the availability of NumPy:
-
-
-try:
- import numpy
-except ImportError:
- pass
-else:
-
- # NumPy numbers do not depend on Variable objects:
- CONSTANT_TYPES += (numpy.number,)
-
- # Entering variables as a block of correlated values. Only available
- # if NumPy is installed.
-
- #! It would be possible to dispense with NumPy, but a routine should be
- # written for obtaining the eigenvectors of a symmetric matrix. See
- # for instance Numerical Recipes: (1) reduction to tri-diagonal
- # [Givens or Householder]; (2) QR / QL decomposition.
-
- def correlated_values(nom_values, covariance_mat, tags=None):
- """
- Returns numbers with uncertainties (AffineScalarFunc objects)
- that correctly reproduce the given covariance matrix, and have
- the given (float) values as their nominal value.
-
- The correlated_values_norm() function returns the same result,
- but takes a correlation matrix instead of a covariance matrix.
-
- The list of values and the covariance matrix must have the
- same length, and the matrix must be a square (symmetric) one.
-
- The numbers with uncertainties returned depend on newly
- created, independent variables (Variable objects).
-
- If 'tags' is not None, it must list the tag of each new
- independent variable.
-
- nom_values -- sequence with the nominal (real) values of the
- numbers with uncertainties to be returned.
-
- covariance_mat -- full covariance matrix of the returned
- numbers with uncertainties (not the statistical correlation
- matrix, i.e., not the normalized covariance matrix). For
- example, the first element of this matrix is the variance of
- the first returned number with uncertainty.
- """
-
- # If no tags were given, we prepare tags for the newly created
- # variables:
- if tags is None:
- tags = (None,) * len(nom_values)
-
- # The covariance matrix is diagonalized in order to define
- # the independent variables that model the given values:
-
- (variances, transform) = numpy.linalg.eigh(covariance_mat)
-
- # Numerical errors might make some variances negative: we set
- # them to zero:
- variances[variances < 0] = 0.
-
- # Creation of new, independent variables:
-
- # We use the fact that the eigenvectors in 'transform' are
- # special: 'transform' is unitary: its inverse is its transpose:
-
- variables = tuple(
- # The variables represent "pure" uncertainties:
- Variable(0, sqrt(variance), tag)
- for (variance, tag) in zip(variances, tags))
-
- # Representation of the initial correlated values:
- values_funcs = tuple(
- AffineScalarFunc(value, dict(zip(variables, coords)))
- for (coords, value) in zip(transform, nom_values))
-
- return values_funcs
-
- __all__.append('correlated_values')
-
- def correlated_values_norm(values_with_std_dev, correlation_mat,
- tags=None):
- '''
- Returns correlated values like correlated_values(), but takes
- instead as input:
-
- - nominal (float) values along with their standard deviation, and
-
- - a correlation matrix (i.e. a normalized covariance matrix
- normalized with individual standard deviations).
-
- values_with_std_dev -- sequence of (nominal value, standard
- deviation) pairs. The returned, correlated values have these
- nominal values and standard deviations.
-
- correlation_mat -- correlation matrix (i.e. the normalized
- covariance matrix, a matrix with ones on its diagonal).
- '''
-
- (nominal_values, std_devs) = numpy.transpose(values_with_std_dev)
-
- return correlated_values(
- nominal_values,
- correlation_mat*std_devs*std_devs[numpy.newaxis].T,
- tags)
-
- __all__.append('correlated_values_norm')
-
-###############################################################################
-
-# Mathematical operations with local approximations (affine scalar
-# functions)
-
-class NotUpcast(Exception):
- 'Raised when an object cannot be converted to a number with uncertainty'
-
-def to_affine_scalar(x):
- """
- Transforms x into a constant affine scalar function
- (AffineScalarFunc), unless it is already an AffineScalarFunc (in
- which case x is returned unchanged).
-
- Raises an exception unless 'x' belongs to some specific classes of
- objects that are known not to depend on AffineScalarFunc objects
- (which then cannot be considered as constants).
- """
-
- if isinstance(x, AffineScalarFunc):
- return x
-
- #! In Python 2.6+, numbers.Number could be used instead, here:
- if isinstance(x, CONSTANT_TYPES):
- # No variable => no derivative to define:
- return AffineScalarFunc(x, {})
-
- # Case of lists, etc.
- raise NotUpcast("%s cannot be converted to a number with"
- " uncertainty" % type(x))
-
-def partial_derivative(f, param_num):
- """
- Returns a function that numerically calculates the partial
- derivative of function f with respect to its argument number
- param_num.
-
- The step parameter represents the shift of the parameter used in
- the numerical approximation.
- """
-
- def partial_derivative_of_f(*args, **kws):
- """
- Partial derivative, calculated with the (-epsilon, +epsilon)
- method, which is more precise than the (0, +epsilon) method.
- """
- # f_nominal_value = f(*args)
- param_kw = None
- if '__param__kw__' in kws:
- param_kw = kws.pop('__param__kw__')
- shifted_args = list(args) # Copy, and conversion to a mutable
- shifted_kws = {}
- for k, v in kws.items():
- shifted_kws[k] = v
- step = 1.e-8
- if param_kw in shifted_kws:
- step = step*abs(shifted_kws[param_kw])
- elif param_num < len(shifted_args):
- # The step is relative to the parameter being varied, so that
- # shsifting it does not suffer from finite precision:
- step = step*abs(shifted_args[param_num])
-
- if param_kw in shifted_kws:
- shifted_kws[param_kw] += step
- elif param_num < len(shifted_args):
- shifted_args[param_num] += step
-
- shifted_f_plus = f(*shifted_args, **shifted_kws)
-
- if param_kw in shifted_kws:
- shifted_kws[param_kw] -= 2*step
- elif param_num < len(shifted_args):
- shifted_args[param_num] -= 2*step
- shifted_f_minus = f(*shifted_args, **shifted_kws)
-
- return (shifted_f_plus - shifted_f_minus)/2/step
-
- return partial_derivative_of_f
-
-class NumericalDerivatives(object):
- """
- Convenient access to the partial derivatives of a function,
- calculated numerically.
- """
- # This is not a list because the number of arguments of the
- # function is not known in advance, in general.
-
- def __init__(self, function):
- """
- 'function' is the function whose derivatives can be computed.
- """
- self._function = function
-
- def __getitem__(self, n):
- """
- Returns the n-th numerical derivative of the function.
- """
- return partial_derivative(self._function, n)
-
-def wrap(f, derivatives_iter=None):
- """
- Wraps a function f into a function that also accepts numbers with
- uncertainties (UFloat objects) and returns a number with
- uncertainties. Doing so may be necessary when function f cannot
- be expressed analytically (with uncertainties-compatible operators
- and functions like +, *, umath.sin(), etc.).
-
- f must return a scalar (not a list, etc.).
-
- In the wrapped function, the standard Python scalar arguments of f
- (float, int, etc.) can be replaced by numbers with
- uncertainties. The result will contain the appropriate
- uncertainty.
-
- If no argument to the wrapped function has an uncertainty, f
- simply returns its usual, scalar result.
-
- If supplied, derivatives_iter can be an iterable that generally
- contains functions; each successive function is the partial
- derivative of f with respect to the corresponding variable (one
- function for each argument of f, which takes as many arguments as
- f). If instead of a function, an element of derivatives_iter
- contains None, then it is automatically replaced by the relevant
- numerical derivative; this can be used for non-scalar arguments of
- f (like string arguments).
-
- If derivatives_iter is None, or if derivatives_iter contains a
- fixed (and finite) number of elements, then any missing derivative
- is calculated numerically.
-
- An infinite number of derivatives can be specified by having
- derivatives_iter be an infinite iterator; this can for instance
- be used for specifying the derivatives of functions with a
- undefined number of argument (like sum(), whose partial
- derivatives all return 1).
-
- Example (for illustration purposes only, as
- uncertainties.umath.sin() runs faster than the examples that
- follow): wrap(math.sin) is a sine function that can be applied to
- numbers with uncertainties. Its derivative will be calculated
- numerically. wrap(math.sin, [None]) would have produced the same
- result. wrap(math.sin, [math.cos]) is the same function, but with
- an analytically defined derivative.
- """
-
- if derivatives_iter is None:
- derivatives_iter = NumericalDerivatives(f)
- else:
- # Derivatives that are not defined are calculated numerically,
- # if there is a finite number of them (the function lambda
- # *args: fsum(args) has a non-defined number of arguments, as
- # it just performs a sum):
- try: # Is the number of derivatives fixed?
- len(derivatives_iter)
- except TypeError:
- pass
- else:
- derivatives_iter = [
- partial_derivative(f, k) if derivative is None
- else derivative
- for (k, derivative) in enumerate(derivatives_iter)]
-
- #! Setting the doc string after "def f_with...()" does not
- # seem to work. We define it explicitly:
- @set_doc("""\
- Version of %s(...) that returns an affine approximation
- (AffineScalarFunc object), if its result depends on variables
- (Variable objects). Otherwise, returns a simple constant (when
- applied to constant arguments).
-
- Warning: arguments of the function that are not AffineScalarFunc
- objects must not depend on uncertainties.Variable objects in any
- way. Otherwise, the dependence of the result in
- uncertainties.Variable objects will be incorrect.
-
- Original documentation:
- %s""" % (f.__name__, f.__doc__))
- def f_with_affine_output(*args, **kwargs):
- # Can this function perform the calculation of an
- # AffineScalarFunc (or maybe float) result?
- try:
- old_funcs = map(to_affine_scalar, args)
- aff_funcs = [to_affine_scalar(a) for a in args]
- aff_kws = kwargs
- aff_varkws = []
- for key, val in kwargs.items():
- if isinstance(val, Variable):
- aff_kws[key] = to_affine_scalar(val)
- aff_varkws.append(key)
-
- except NotUpcast:
-
- # This function does not know how to itself perform
- # calculations with non-float-like arguments (as they
- # might for instance be objects whose value really changes
- # if some Variable objects had different values):
-
- # Is it clear that we can't delegate the calculation?
-
- if any(isinstance(arg, AffineScalarFunc) for arg in args):
- # This situation arises for instance when calculating
- # AffineScalarFunc(...)*numpy.array(...). In this
- # case, we must let NumPy handle the multiplication
- # (which is then performed element by element):
- return NotImplemented
- else:
- # If none of the arguments is an AffineScalarFunc, we
- # can delegate the calculation to the original
- # function. This can be useful when it is called with
- # only one argument (as in
- # numpy.log10(numpy.ndarray(...)):
- return f(*args, **kwargs)
-
- ########################################
- # Nominal value of the constructed AffineScalarFunc:
- args_values = [e.nominal_value for e in aff_funcs]
- kw_values = {}
- for key, val in aff_kws.items():
- kw_values[key] = val
- if key in aff_varkws:
- kw_values[key] = val.nominal_value
- f_nominal_value = f(*args_values, **kw_values)
-
- ########################################
-
- # List of involved variables (Variable objects):
- variables = set()
- for expr in aff_funcs:
- variables |= set(expr.derivatives)
- for vname in aff_varkws:
- variables |= set(aff_kws[vname].derivatives)
- ## It is sometimes useful to only return a regular constant:
-
- # (1) Optimization / convenience behavior: when 'f' is called
- # on purely constant values (e.g., sin(2)), there is no need
- # for returning a more complex AffineScalarFunc object.
-
- # (2) Functions that do not return a "float-like" value might
- # not have a relevant representation as an AffineScalarFunc.
- # This includes boolean functions, since their derivatives are
- # either 0 or are undefined: they are better represented as
- # Python constants than as constant AffineScalarFunc functions.
-
- if not variables or isinstance(f_nominal_value, bool):
- return f_nominal_value
-
- # The result of 'f' does depend on 'variables'...
-
- ########################################
-
- # Calculation of the derivatives with respect to the arguments
- # of f (aff_funcs):
-
- # The chain rule is applied. This is because, in the case of
- # numerical derivatives, it allows for a better-controlled
- # numerical stability than numerically calculating the partial
- # derivatives through '[f(x + dx, y + dy, ...) -
- # f(x,y,...)]/da' where dx, dy,... are calculated by varying
- # 'a'. In fact, it is numerically better to control how big
- # (dx, dy,...) are: 'f' is a simple mathematical function and
- # it is possible to know how precise the df/dx are (which is
- # not possible with the numerical df/da calculation above).
-
- # We use numerical derivatives, if we don't already have a
- # list of derivatives:
-
- #! Note that this test could be avoided by requiring the
- # caller to always provide derivatives. When changing the
- # functions of the math module, this would force this module
- # to know about all the math functions. Another possibility
- # would be to force derivatives_iter to contain, say, the
- # first 3 derivatives of f. But any of these two ideas has a
- # chance to break, one day... (if new functions are added to
- # the math module, or if some function has more than 3
- # arguments).
-
- derivatives_wrt_args = []
- for (arg, derivative) in zip(aff_funcs, derivatives_iter):
- derivatives_wrt_args.append(derivative(*args_values, **aff_kws)
- if arg.derivatives
- else 0)
-
-
- kws_values = []
- for vname in aff_varkws:
- kws_values.append( aff_kws[vname].nominal_value)
- for (vname, derivative) in zip(aff_varkws, derivatives_iter):
- derivatives_wrt_args.append(derivative(__param__kw__=vname,
- **kw_values)
- if aff_kws[vname].derivatives
- else 0)
-
- ########################################
- # Calculation of the derivative of f with respect to all the
- # variables (Variable) involved.
-
- # Initial value (is updated below):
- derivatives_wrt_vars = dict((var, 0.) for var in variables)
-
- # The chain rule is used (we already have
- # derivatives_wrt_args):
-
- for (func, f_derivative) in zip(aff_funcs, derivatives_wrt_args):
- for (var, func_derivative) in func.derivatives.items():
- derivatives_wrt_vars[var] += f_derivative * func_derivative
-
- for (vname, f_derivative) in zip(aff_varkws, derivatives_wrt_args):
- func = aff_kws[vname]
- for (var, func_derivative) in func.derivatives.items():
- derivatives_wrt_vars[var] += f_derivative * func_derivative
-
- # The function now returns an AffineScalarFunc object:
- return AffineScalarFunc(f_nominal_value, derivatives_wrt_vars)
-
- # It is easier to work with f_with_affine_output, which represents
- # a wrapped version of 'f', when it bears the same name as 'f':
- f_with_affine_output.__name__ = f.__name__
-
- return f_with_affine_output
-
-def _force_aff_func_args(func):
- """
- Takes an operator op(x, y) and wraps it.
-
- The constructed operator returns func(x, to_affine_scalar(y)) if y
- can be upcast with to_affine_scalar(); otherwise, it returns
- NotImplemented.
-
- Thus, func() is only called on two AffineScalarFunc objects, if
- its first argument is an AffineScalarFunc.
- """
-
- def op_on_upcast_args(x, y):
- """
- Returns %s(self, to_affine_scalar(y)) if y can be upcast
- through to_affine_scalar. Otherwise returns NotImplemented.
- """ % func.__name__
-
- try:
- y_with_uncert = to_affine_scalar(y)
- except NotUpcast:
- # This module does not know how to handle the comparison:
- # (example: y is a NumPy array, in which case the NumPy
- # array will decide that func() should be applied
- # element-wise between x and all the elements of y):
- return NotImplemented
- else:
- return func(x, y_with_uncert)
-
- return op_on_upcast_args
-
-########################################
-
-# Definition of boolean operators, that assume that self and
-# y_with_uncert are AffineScalarFunc.
-
-# The fact that uncertainties must be smalled is used, here: the
-# comparison functions are supposed to be constant for most values of
-# the random variables.
-
-# Even though uncertainties are supposed to be small, comparisons
-# between 3+/-0.1 and 3.0 are handled (even though x == 3.0 is not a
-# constant function in the 3+/-0.1 interval). The comparison between
-# x and x is handled too, when x has an uncertainty. In fact, as
-# explained in the main documentation, it is possible to give a useful
-# meaning to the comparison operators, in these cases.
-
-def _eq_on_aff_funcs(self, y_with_uncert):
- """
- __eq__ operator, assuming that both self and y_with_uncert are
- AffineScalarFunc objects.
- """
- difference = self - y_with_uncert
- # Only an exact zero difference means that self and y are
- # equal numerically:
- return not(difference._nominal_value or difference.std_dev())
-
-def _ne_on_aff_funcs(self, y_with_uncert):
- """
- __ne__ operator, assuming that both self and y_with_uncert are
- AffineScalarFunc objects.
- """
-
- return not _eq_on_aff_funcs(self, y_with_uncert)
-
-def _gt_on_aff_funcs(self, y_with_uncert):
- """
- __gt__ operator, assuming that both self and y_with_uncert are
- AffineScalarFunc objects.
- """
- return self._nominal_value > y_with_uncert._nominal_value
-
-def _ge_on_aff_funcs(self, y_with_uncert):
- """
- __ge__ operator, assuming that both self and y_with_uncert are
- AffineScalarFunc objects.
- """
-
- return (_gt_on_aff_funcs(self, y_with_uncert)
- or _eq_on_aff_funcs(self, y_with_uncert))
-
-def _lt_on_aff_funcs(self, y_with_uncert):
- """
- __lt__ operator, assuming that both self and y_with_uncert are
- AffineScalarFunc objects.
- """
- return self._nominal_value < y_with_uncert._nominal_value
-
-def _le_on_aff_funcs(self, y_with_uncert):
- """
- __le__ operator, assuming that both self and y_with_uncert are
- AffineScalarFunc objects.
- """
-
- return (_lt_on_aff_funcs(self, y_with_uncert)
- or _eq_on_aff_funcs(self, y_with_uncert))
-
-########################################
-
-class AffineScalarFunc(object):
- """
- Affine functions that support basic mathematical operations
- (addition, etc.). Such functions can for instance be used for
- representing the local (linear) behavior of any function.
-
- This class is mostly meant to be used internally.
-
- This class can also be used to represent constants.
-
- The variables of affine scalar functions are Variable objects.
-
- AffineScalarFunc objects include facilities for calculating the
- 'error' on the function, from the uncertainties on its variables.
-
- Main attributes and methods:
-
- - nominal_value, std_dev(): value at the origin / nominal value,
- and standard deviation.
-
- - error_components(): error_components()[x] is the error due to
- Variable x.
-
- - derivatives: derivatives[x] is the (value of the) derivative
- with respect to Variable x. This attribute is a dictionary
- whose keys are the Variable objects on which the function
- depends.
-
- All the Variable objects on which the function depends are in
- 'derivatives'.
-
- - std_score(x): position of number x with respect to the
- nominal value, in units of the standard deviation.
- """
-
- # To save memory in large arrays:
- __slots__ = ('_nominal_value', 'derivatives')
-
- #! The code could be modify in order to accommodate for non-float
- # nominal values. This could for instance be done through
- # the operator module: instead of delegating operations to
- # float.__*__ operations, they could be delegated to
- # operator.__*__ functions (while taking care of properly handling
- # reverse operations: __radd__, etc.).
-
- def __init__(self, nominal_value, derivatives):
- """
- nominal_value -- value of the function at the origin.
- nominal_value must not depend in any way of the Variable
- objects in 'derivatives' (the value at the origin of the
- function being defined is a constant).
-
- derivatives -- maps each Variable object on which the function
- being defined depends to the value of the derivative with
- respect to that variable, taken at the nominal value of all
- variables.
-
- Warning: the above constraint is not checked, and the user is
- responsible for complying with it.
- """
-
- # Defines the value at the origin:
-
- # Only float-like values are handled. One reason is that it
- # does not make sense for a scalar function to be affine to
- # not yield float values. Another reason is that it would not
- # make sense to have a complex nominal value, here (it would
- # not be handled correctly at all): converting to float should
- # be possible.
- self._nominal_value = float(nominal_value)
- self.derivatives = derivatives
-
- # The following prevents the 'nominal_value' attribute from being
- # modified by the user:
- @property
- def nominal_value(self):
- "Nominal value of the random number."
- return self._nominal_value
-
- ############################################################
-
-
- ### Operators: operators applied to AffineScalarFunc and/or
- ### float-like objects only are supported. This is why methods
- ### from float are used for implementing these operators.
-
- # Operators with no reflection:
-
- ########################################
-
- # __nonzero__() is supposed to return a boolean value (it is used
- # by bool()). It is for instance used for converting the result
- # of comparison operators to a boolean, in sorted(). If we want
- # to be able to sort AffineScalarFunc objects, __nonzero__ cannot
- # return a AffineScalarFunc object. Since boolean results (such
- # as the result of bool()) don't have a very meaningful
- # uncertainty unless it is zero, this behavior is fine.
-
- def __nonzero__(self):
- """
- Equivalent to self != 0.
- """
- #! This might not be relevant for AffineScalarFunc objects
- # that contain values in a linear space which does not convert
- # the float 0 into the null vector (see the __eq__ function:
- # __nonzero__ works fine if subtracting the 0 float from a
- # vector of the linear space works as if 0 were the null
- # vector of that space):
- return self != 0. # Uses the AffineScalarFunc.__ne__ function
-
- ########################################
-
- ## Logical operators: warning: the resulting value cannot always
- ## be differentiated.
-
- # The boolean operations are not differentiable everywhere, but
- # almost...
-
- # (1) I can rely on the assumption that the user only has "small"
- # errors on variables, as this is used in the calculation of the
- # standard deviation (which performs linear approximations):
-
- # (2) However, this assumption is not relevant for some
- # operations, and does not have to hold, in some cases. This
- # comes from the fact that logical operations (e.g. __eq__(x,y))
- # are not differentiable for many usual cases. For instance, it
- # is desirable to have x == x for x = n+/-e, whatever the size of e.
- # Furthermore, n+/-e != n+/-e', if e != e', whatever the size of e or
- # e'.
-
- # (3) The result of logical operators does not have to be a
- # function with derivatives, as these derivatives are either 0 or
- # don't exist (i.e., the user should probably not rely on
- # derivatives for his code).
-
- # __eq__ is used in "if data in [None, ()]", for instance. It is
- # therefore important to be able to handle this case too, which is
- # taken care of when _force_aff_func_args(_eq_on_aff_funcs)
- # returns NotImplemented.
- __eq__ = _force_aff_func_args(_eq_on_aff_funcs)
-
- __ne__ = _force_aff_func_args(_ne_on_aff_funcs)
- __gt__ = _force_aff_func_args(_gt_on_aff_funcs)
-
- # __ge__ is not the opposite of __lt__ because these operators do
- # not always yield a boolean (for instance, 0 <= numpy.arange(10)
- # yields an array).
- __ge__ = _force_aff_func_args(_ge_on_aff_funcs)
-
- __lt__ = _force_aff_func_args(_lt_on_aff_funcs)
- __le__ = _force_aff_func_args(_le_on_aff_funcs)
-
- ########################################
-
- # Uncertainties handling:
-
- def error_components(self):
- """
- Individual components of the standard deviation of the affine
- function (in absolute value), returned as a dictionary with
- Variable objects as keys.
-
- This method assumes that the derivatives contained in the
- object take scalar values (and are not a tuple, like what
- math.frexp() returns, for instance).
- """
-
- # Calculation of the variance:
- error_components = {}
- for (variable, derivative) in self.derivatives.items():
- # Individual standard error due to variable:
- error_components[variable] = abs(derivative*variable._std_dev)
-
- return error_components
-
- def std_dev(self):
- """
- Standard deviation of the affine function.
-
- This method assumes that the function returns scalar results.
-
- This returned standard deviation depends on the current
- standard deviations [std_dev()] of the variables (Variable
- objects) involved.
- """
- #! It would be possible to not allow the user to update the
- #std dev of Variable objects, in which case AffineScalarFunc
- #objects could have a pre-calculated or, better, cached
- #std_dev value (in fact, many intermediate AffineScalarFunc do
- #not need to have their std_dev calculated: only the final
- #AffineScalarFunc returned to the user does).
- return sqrt(sum(
- delta**2 for delta in self.error_components().values()))
-
- def _general_representation(self, to_string):
- """
- Uses the to_string() conversion function on both the nominal
- value and the standard deviation, and returns a string that
- describes them.
-
- to_string() is typically repr() or str().
- """
-
- (nominal_value, std_dev) = (self._nominal_value, self.std_dev())
-
- # String representation:
-
- # Not putting spaces around "+/-" helps with arrays of
- # Variable, as each value with an uncertainty is a
- # block of signs (otherwise, the standard deviation can be
- # mistaken for another element of the array).
-
- return ("%s+/-%s" % (to_string(nominal_value), to_string(std_dev))
- if std_dev
- else to_string(nominal_value))
-
- def __repr__(self):
- return self._general_representation(repr)
-
- def __str__(self):
- return self._general_representation(str)
-
- def std_score(self, value):
- """
- Returns 'value' - nominal value, in units of the standard
- deviation.
-
- Raises a ValueError exception if the standard deviation is zero.
- """
- try:
- # The ._nominal_value is a float: there is no integer division,
- # here:
- return (value - self._nominal_value) / self.std_dev()
- except ZeroDivisionError:
- raise ValueError("The standard deviation is zero:"
- " undefined result.")
-
- def __deepcopy__(self, memo):
- """
- Hook for the standard copy module.
-
- The returned AffineScalarFunc is a completely fresh copy,
- which is fully independent of any variable defined so far.
- New variables are specially created for the returned
- AffineScalarFunc object.
- """
- return AffineScalarFunc(
- self._nominal_value,
- dict((copy.deepcopy(var), deriv)
- for (var, deriv) in self.derivatives.items()))
-
- def __getstate__(self):
- """
- Hook for the pickle module.
- """
- obj_slot_values = dict((k, getattr(self, k)) for k in
- # self.__slots__ would not work when
- # self is an instance of a subclass:
- AffineScalarFunc.__slots__)
- return obj_slot_values
-
- def __setstate__(self, data_dict):
- """
- Hook for the pickle module.
- """
- for (name, value) in data_dict.items():
- setattr(self, name, value)
-
-# Nicer name, for users: isinstance(ufloat(...), UFloat) is True:
-UFloat = AffineScalarFunc
-
-def get_ops_with_reflection():
-
- """
- Returns operators with a reflection, along with their derivatives
- (for float operands).
- """
-
- # Operators with a reflection:
-
- # We do not include divmod(). This operator could be included, by
- # allowing its result (a tuple) to be differentiated, in
- # derivative_value(). However, a similar result can be achieved
- # by the user by calculating separately the division and the
- # result.
-
- # {operator(x, y): (derivative wrt x, derivative wrt y)}:
-
- # Note that unknown partial derivatives can be numerically
- # calculated by expressing them as something like
- # "partial_derivative(float.__...__, 1)(x, y)":
-
- # String expressions are used, so that reversed operators are easy
- # to code, and execute relatively efficiently:
-
- derivatives_list = {
- 'add': ("1.", "1."),
- # 'div' is the '/' operator when __future__.division is not in
- # effect. Since '/' is applied to
- # AffineScalarFunc._nominal_value numbers, it is applied on
- # floats, and is therefore the "usual" mathematical division.
- 'div': ("1/y", "-x/y**2"),
- 'floordiv': ("0.", "0."), # Non exact: there is a discontinuities
- # The derivative wrt the 2nd arguments is something like (..., x//y),
- # but it is calculated numerically, for convenience:
- 'mod': ("1.", "partial_derivative(float.__mod__, 1)(x, y)"),
- 'mul': ("y", "x"),
- 'pow': ("y*x**(y-1)", "log(x)*x**y"),
- 'sub': ("1.", "-1."),
- 'truediv': ("1/y", "-x/y**2")
- }
-
- # Conversion to Python functions:
- ops_with_reflection = {}
- for (op, derivatives) in derivatives_list.items():
- ops_with_reflection[op] = [
- eval("lambda x, y: %s" % expr) for expr in derivatives ]
-
- ops_with_reflection["r"+op] = [
- eval("lambda y, x: %s" % expr) for expr in reversed(derivatives)]
-
- return ops_with_reflection
-
-# Operators that have a reflection, along with their derivatives:
-_ops_with_reflection = get_ops_with_reflection()
-
-# Some effectively modified operators (for the automated tests):
-_modified_operators = []
-_modified_ops_with_reflection = []
-
-def add_operators_to_AffineScalarFunc():
- """
- Adds many operators (__add__, etc.) to the AffineScalarFunc class.
- """
-
- ########################################
-
- #! Derivatives are set to return floats. For one thing,
- # uncertainties generally involve floats, as they are based on
- # small variations of the parameters. It is also better to
- # protect the user from unexpected integer result that behave
- # badly with the division.
-
- ## Operators that return a numerical value:
-
- # Single-argument operators that should be adapted from floats to
- # AffineScalarFunc objects, associated to their derivative:
- simple_numerical_operators_derivatives = {
- 'abs': lambda x: 1. if x>=0 else -1.,
- 'neg': lambda x: -1.,
- 'pos': lambda x: 1.,
- 'trunc': lambda x: 0.
- }
-
- for (op, derivative) in (
- simple_numerical_operators_derivatives.items()):
-
- attribute_name = "__%s__" % op
- # float objects don't exactly have the same attributes between
- # different versions of Python (for instance, __trunc__ was
- # introduced with Python 2.6):
- try:
- setattr(AffineScalarFunc, attribute_name,
- wrap(getattr(float, attribute_name),
- [derivative]))
- except AttributeError:
- pass
- else:
- _modified_operators.append(op)
-
- ########################################
-
- # Reversed versions (useful for float*AffineScalarFunc, for instance):
- for (op, derivatives) in _ops_with_reflection.items():
- attribute_name = '__%s__' % op
- # float objects don't exactly have the same attributes between
- # different versions of Python (for instance, __div__ and
- # __rdiv__ were removed, in Python 3):
- try:
- setattr(AffineScalarFunc, attribute_name,
- wrap(getattr(float, attribute_name), derivatives))
- except AttributeError:
- pass
- else:
- _modified_ops_with_reflection.append(op)
-
- ########################################
- # Conversions to pure numbers are meaningless. Note that the
- # behavior of float(1j) is similar.
- for coercion_type in ('complex', 'int', 'long', 'float'):
- def raise_error(self):
- raise TypeError("can't convert an affine function (%s)"
- ' to %s; use x.nominal_value'
- # In case AffineScalarFunc is sub-classed:
- % (self.__class__, coercion_type))
-
- setattr(AffineScalarFunc, '__%s__' % coercion_type, raise_error)
-
-add_operators_to_AffineScalarFunc() # Actual addition of class attributes
-
-class Variable(AffineScalarFunc):
- """
- Representation of a float-like scalar random variable, along with
- its uncertainty.
-
- Objects are meant to represent variables that are independent from
- each other (correlations are handled through the AffineScalarFunc
- class).
- """
-
- # To save memory in large arrays:
- __slots__ = ('_std_dev', 'tag')
-
- def __init__(self, value, std_dev, tag=None):
- """
- The nominal value and the standard deviation of the variable
- are set. These values must be scalars.
-
- 'tag' is a tag that the user can associate to the variable. This
- is useful for tracing variables.
-
- The meaning of the nominal value is described in the main
- module documentation.
- """
-
- #! The value, std_dev, and tag are assumed by __copy__() not to
- # be copied. Either this should be guaranteed here, or __copy__
- # should be updated.
-
- # Only float-like values are handled. One reason is that the
- # division operator on integers would not produce a
- # differentiable functions: for instance, Variable(3, 0.1)/2
- # has a nominal value of 3/2 = 1, but a "shifted" value
- # of 3.1/2 = 1.55.
- value = float(value)
-
- # If the variable changes by dx, then the value of the affine
- # function that gives its value changes by 1*dx:
-
- # ! Memory cycles are created. However, they are garbage
- # collected, if possible. Using a weakref.WeakKeyDictionary
- # takes much more memory. Thus, this implementation chooses
- # more cycles and a smaller memory footprint instead of no
- # cycles and a larger memory footprint.
-
- # ! Using AffineScalarFunc instead of super() results only in
- # a 3 % speed loss (Python 2.6, Mac OS X):
- super(Variable, self).__init__(value, {self: 1.})
-
- # We force the error to be float-like. Since it is considered
- # as a Gaussian standard deviation, it is semantically
- # positive (even though there would be no problem defining it
- # as a sigma, where sigma can be negative and still define a
- # Gaussian):
-
- assert std_dev >= 0, "the error must be a positive number"
- # Since AffineScalarFunc.std_dev is a property, we cannot do
- # "self.std_dev = ...":
- self._std_dev = std_dev
-
- self.tag = tag
-
- # Standard deviations can be modified (this is a feature).
- # AffineScalarFunc objects that depend on the Variable have their
- # std_dev() automatically modified (recalculated with the new
- # std_dev of their Variables):
- def set_std_dev(self, value):
- """
- Updates the standard deviation of the variable to a new value.
- """
-
- # A zero variance is accepted. Thus, it is possible to
- # conveniently use infinitely precise variables, for instance
- # to study special cases.
-
- self._std_dev = value
-
- # The following method is overridden so that we can represent the tag:
- def _general_representation(self, to_string):
- """
- Uses the to_string() conversion function on both the nominal
- value and standard deviation and returns a string that
- describes the number.
-
- to_string() is typically repr() or str().
- """
- num_repr = super(Variable, self)._general_representation(to_string)
-
- # Optional tag: only full representations (to_string == repr)
- # contain the tag, as the tag is required in order to recreate
- # the variable. Outputting the tag for regular string ("print
- # x") would be too heavy and produce an unusual representation
- # of a number with uncertainty.
- return (num_repr if ((self.tag is None) or (to_string != repr))
- else "< %s = %s >" % (self.tag, num_repr))
-
- def __hash__(self):
- # All Variable objects are by definition independent
- # variables, so they never compare equal; therefore, their
- # id() are therefore allowed to differ
- # (http://docs.python.org/reference/datamodel.html#object.__hash__):
- return id(self)
-
- def __copy__(self):
- """
- Hook for the standard copy module.
- """
-
- # This copy implicitly takes care of the reference of the
- # variable to itself (in self.derivatives): the new Variable
- # object points to itself, not to the original Variable.
-
- # Reference: http://www.doughellmann.com/PyMOTW/copy/index.html
-
- #! The following assumes that the arguments to Variable are
- # *not* copied upon construction, since __copy__ is not supposed
- # to copy "inside" information:
- return Variable(self.nominal_value, self.std_dev(), self.tag)
-
- def __deepcopy__(self, memo):
- """
- Hook for the standard copy module.
-
- A new variable is created.
- """
-
- # This deep copy implicitly takes care of the reference of the
- # variable to itself (in self.derivatives): the new Variable
- # object points to itself, not to the original Variable.
-
- # Reference: http://www.doughellmann.com/PyMOTW/copy/index.html
-
- return self.__copy__()
-
- def __getstate__(self):
- """
- Hook for the standard pickle module.
- """
- obj_slot_values = dict((k, getattr(self, k)) for k in self.__slots__)
- obj_slot_values.update(AffineScalarFunc.__getstate__(self))
- # Conversion to a usual dictionary:
- return obj_slot_values
-
- def __setstate__(self, data_dict):
- """
- Hook for the standard pickle module.
- """
- for (name, value) in data_dict.items():
- setattr(self, name, value)
-
-###############################################################################
-
-# Utilities
-
-def nominal_value(x):
- """
- Returns the nominal value of x if it is a quantity with
- uncertainty (i.e., an AffineScalarFunc object); otherwise, returns
- x unchanged.
-
- This utility function is useful for transforming a series of
- numbers, when only some of them generally carry an uncertainty.
- """
-
- return x.nominal_value if isinstance(x, AffineScalarFunc) else x
-
-def std_dev(x):
- """
- Returns the standard deviation of x if it is a quantity with
- uncertainty (i.e., an AffineScalarFunc object); otherwise, returns
- the float 0.
-
- This utility function is useful for transforming a series of
- numbers, when only some of them generally carry an uncertainty.
- """
-
- return x.std_dev() if isinstance(x, AffineScalarFunc) else 0.
-
-def covariance_matrix(nums_with_uncert):
- """
- Returns a matrix that contains the covariances between the given
- sequence of numbers with uncertainties (AffineScalarFunc objects).
- The resulting matrix implicitly depends on their ordering in
- 'nums_with_uncert'.
-
- The covariances are floats (never int objects).
-
- The returned covariance matrix is the exact linear approximation
- result, if the nominal values of the numbers with uncertainties
- and of their variables are their mean. Otherwise, the returned
- covariance matrix should be close to its linear approximation
- value.
-
- The returned matrix is a list of lists.
- """
- # See PSI.411 in EOL's notes.
-
- covariance_matrix = []
- for (i1, expr1) in enumerate(nums_with_uncert):
- derivatives1 = expr1.derivatives # Optimization
- vars1 = set(derivatives1)
- coefs_expr1 = []
- for (i2, expr2) in enumerate(nums_with_uncert[:i1+1]):
- derivatives2 = expr2.derivatives # Optimization
- coef = 0.
- for var in vars1.intersection(derivatives2):
- # var is a variable common to both numbers with
- # uncertainties:
- coef += (derivatives1[var]*derivatives2[var]*var._std_dev**2)
- coefs_expr1.append(coef)
- covariance_matrix.append(coefs_expr1)
-
- # We symmetrize the matrix:
- for (i, covariance_coefs) in enumerate(covariance_matrix):
- covariance_coefs.extend(covariance_matrix[j][i]
- for j in range(i+1, len(covariance_matrix)))
-
- return covariance_matrix
-
-try:
- import numpy
-except ImportError:
- pass
-else:
- def correlation_matrix(nums_with_uncert):
- '''
- Returns the correlation matrix of the given sequence of
- numbers with uncertainties, as a NumPy array of floats.
- '''
-
- cov_mat = numpy.array(covariance_matrix(nums_with_uncert))
-
- std_devs = numpy.sqrt(cov_mat.diagonal())
-
- return cov_mat/std_devs/std_devs[numpy.newaxis].T
-
- __all__.append('correlation_matrix')
-
-###############################################################################
-# Parsing of values with uncertainties:
-
-POSITIVE_DECIMAL_UNSIGNED = r'(\d+)(\.\d*)?'
-
-# Regexp for a number with uncertainty (e.g., "-1.234(2)e-6"), where the
-# uncertainty is optional (in which case the uncertainty is implicit):
-NUMBER_WITH_UNCERT_RE_STR = '''
- ([+-])? # Sign
- %s # Main number
- (?:\(%s\))? # Optional uncertainty
- ([eE][+-]?\d+)? # Optional exponent
- ''' % (POSITIVE_DECIMAL_UNSIGNED, POSITIVE_DECIMAL_UNSIGNED)
-
-NUMBER_WITH_UNCERT_RE = re.compile(
- "^%s$" % NUMBER_WITH_UNCERT_RE_STR, re.VERBOSE)
-
-def parse_error_in_parentheses(representation):
- """
- Returns (value, error) from a string representing a number with
- uncertainty like 12.34(5), 12.34(142), 12.5(3.4) or 12.3(4.2)e3.
- If no parenthesis is given, an uncertainty of one on the last
- digit is assumed.
-
- Raises ValueError if the string cannot be parsed.
- """
-
- match = NUMBER_WITH_UNCERT_RE.search(representation)
-
- if match:
- # The 'main' part is the nominal value, with 'int'eger part, and
- # 'dec'imal part. The 'uncert'ainty is similarly broken into its
- # integer and decimal parts.
- (sign, main_int, main_dec, uncert_int, uncert_dec,
- exponent) = match.groups()
- else:
- raise ValueError("Unparsable number representation: '%s'."
- " Was expecting a string of the form 1.23(4)"
- " or 1.234" % representation)
-
- # The value of the number is its nominal value:
- value = float(''.join((sign or '',
- main_int,
- main_dec or '.0',
- exponent or '')))
-
- if uncert_int is None:
- # No uncertainty was found: an uncertainty of 1 on the last
- # digit is assumed:
- uncert_int = '1'
-
- # Do we have a fully explicit uncertainty?
- if uncert_dec is not None:
- uncert = float("%s%s" % (uncert_int, uncert_dec or ''))
- else:
- # uncert_int represents an uncertainty on the last digits:
-
- # The number of digits after the period defines the power of
- # 10 than must be applied to the provided uncertainty:
- num_digits_after_period = (0 if main_dec is None
- else len(main_dec)-1)
- uncert = int(uncert_int)/10**num_digits_after_period
-
- # We apply the exponent to the uncertainty as well:
- uncert *= float("1%s" % (exponent or ''))
-
- return (value, uncert)
-
-
-# The following function is not exposed because it can in effect be
-# obtained by doing x = ufloat(representation) and
-# x.nominal_value and x.std_dev():
-def str_to_number_with_uncert(representation):
- """
- Given a string that represents a number with uncertainty, returns the
- nominal value and the uncertainty.
-
- The string can be of the form:
- - 124.5+/-0.15
- - 124.50(15)
- - 124.50(123)
- - 124.5
-
- When no numerical error is given, an uncertainty of 1 on the last
- digit is implied.
-
- Raises ValueError if the string cannot be parsed.
- """
-
- try:
- # Simple form 1234.45+/-1.2:
- (value, uncert) = representation.split('+/-')
- except ValueError:
- # Form with parentheses or no uncertainty:
- parsed_value = parse_error_in_parentheses(representation)
- else:
- try:
- parsed_value = (float(value), float(uncert))
- except ValueError:
- raise ValueError('Cannot parse %s: was expecting a number'
- ' like 1.23+/-0.1' % representation)
-
- return parsed_value
-
-def ufloat(representation, tag=None):
- """
- Returns a random variable (Variable object).
-
- Converts the representation of a number into a number with
- uncertainty (a random variable, defined by a nominal value and
- a standard deviation).
-
- The representation can be a (value, standard deviation) sequence,
- or a string.
-
- Strings of the form '12.345+/-0.015', '12.345(15)', or '12.3' are
- recognized (see full list below). In the last case, an
- uncertainty of +/-1 is assigned to the last digit.
-
- 'tag' is an optional string tag for the variable. Variables
- don't have to have distinct tags. Tags are useful for tracing
- what values (and errors) enter in a given result (through the
- error_components() method).
-
- Examples of valid string representations:
-
- -1.23(3.4)
- -1.34(5)
- 1(6)
- 3(4.2)
- -9(2)
- 1234567(1.2)
- 12.345(15)
- -12.3456(78)e-6
- 12.3(0.4)e-5
- 0.29
- 31.
- -31.
- 31
- -3.1e10
- 169.0(7)
- 169.1(15)
- """
-
- # This function is somewhat optimized so as to help with the
- # creation of lots of Variable objects (through unumpy.uarray, for
- # instance).
-
- # representations is "normalized" so as to be a valid sequence of
- # 2 arguments for Variable().
-
- #! Accepting strings and any kind of sequence slows down the code
- # by about 5 %. On the other hand, massive initializations of
- # numbers with uncertainties are likely to be performed with
- # unumpy.uarray, which does not support parsing from strings and
- # thus does not have any overhead.
-
- #! Different, in Python 3:
- if isinstance(representation, basestring):
- representation = str_to_number_with_uncert(representation)
-
- #! The tag is forced to be a string, so that the user does not
- # create a Variable(2.5, 0.5) in order to represent 2.5 +/- 0.5.
- # Forcing 'tag' to be a string prevents numerical uncertainties
- # from being considered as tags, here:
- if tag is not None:
- #! 'unicode' is removed in Python3:
- assert isinstance(tag, (str, unicode)), "The tag can only be a string."
-
- #! The special ** syntax is for Python 2.5 and before (Python 2.6+
- # understands tag=tag):
- return Variable(*representation, **{'tag': tag})
-
+#!! Whenever the documentation below is updated, setup.py should be
+# checked for consistency.
+
+'''
+Calculations with full error propagation for quantities with uncertainties.
+Derivatives can also be calculated.
+
+Web user guide: http://packages.python.org/uncertainties/.
+
+Example of possible calculation: (0.2 +/- 0.01)**2 = 0.04 +/- 0.004.
+
+Correlations between expressions are correctly taken into account (for
+instance, with x = 0.2+/-0.01, 2*x-x-x is exactly zero, as is y-x-x
+with y = 2*x).
+
+Examples:
+
+ import uncertainties
+ from uncertainties import ufloat
+ from uncertainties.umath import * # sin(), etc.
+
+ # Mathematical operations:
+ x = ufloat((0.20, 0.01)) # x = 0.20+/-0.01
+ x = ufloat("0.20+/-0.01") # Other representation
+ x = ufloat("0.20(1)") # Other representation
+ x = ufloat("0.20") # Implicit uncertainty of +/-1 on the last digit
+ print x**2 # Square: prints "0.04+/-0.004"
+ print sin(x**2) # Prints "0.0399...+/-0.00399..."
+
+ print x.std_score(0.17) # Prints "-3.0": deviation of -3 sigmas
+
+ # Access to the nominal value, and to the uncertainty:
+ square = x**2 # Square
+ print square # Prints "0.04+/-0.004"
+ print square.nominal_value # Prints "0.04"
+ print square.std_dev() # Prints "0.004..."
+
+ print square.derivatives[x] # Partial derivative: 0.4 (= 2*0.20)
+
+ # Correlations:
+ u = ufloat((1, 0.05), "u variable") # Tag
+ v = ufloat((10, 0.1), "v variable")
+ sum_value = u+v
+
+ u.set_std_dev(0.1) # Standard deviations can be updated on the fly
+ print sum_value - u - v # Prints "0.0" (exact result)
+
+ # List of all sources of error:
+ print sum_value # Prints "11+/-0.1414..."
+ for (var, error) in sum_value.error_components().items():
+ print "%s: %f" % (var.tag, error) # Individual error components
+
+ # Covariance matrices:
+ cov_matrix = uncertainties.covariance_matrix([u, v, sum_value])
+ print cov_matrix # 3x3 matrix
+
+ # Correlated variables can be constructed from a covariance matrix, if
+ # NumPy is available:
+ (u2, v2, sum2) = uncertainties.correlated_values([1, 10, 11],
+ cov_matrix)
+ print u2 # Value and uncertainty of u: correctly recovered (1+/-0.1)
+ print uncertainties.covariance_matrix([u2, v2, sum2]) # == cov_matrix
+
+- The main function provided by this module is ufloat, which creates
+numbers with uncertainties (Variable objects). Variable objects can
+be used as if they were regular Python numbers. The main attributes
+and methods of Variable objects are defined in the documentation of
+the Variable class.
+
+- Valid operations on numbers with uncertainties include basic
+mathematical functions (addition, etc.).
+
+Most operations from the standard math module (sin, etc.) can be applied
+on numbers with uncertainties by using their generalization from the
+uncertainties.umath module:
+
+ from uncertainties.umath import sin
+ print sin(ufloat("1+/-0.01")) # 0.841...+/-0.005...
+ print sin(1) # umath.sin() also works on floats, exactly like math.sin()
+
+Logical operations (>, ==, etc.) are also supported.
+
+Basic operations on NumPy arrays or matrices of numbers with
+uncertainties can be performed:
+
+ 2*numpy.array([ufloat((1, 0.01)), ufloat((2, 0.1))])
+
+More complex operations on NumPy arrays can be performed through the
+dedicated uncertainties.unumpy sub-module (see its documentation).
+
+Calculations that are performed through non-Python code (Fortran, C,
+etc.) can handle numbers with uncertainties instead of floats through
+the provided wrap() wrapper:
+
+ import uncertainties
+
+ # wrapped_f is a version of f that can take arguments with
+ # uncertainties, even if f only takes floats:
+ wrapped_f = uncertainties.wrap(f)
+
+If some derivatives of the wrapped function f are known (analytically,
+or numerically), they can be given to wrap()--see the documentation
+for wrap().
+
+- Utility functions are also provided: the covariance matrix between
+random variables can be calculated with covariance_matrix(), or used
+as input for the definition of correlated quantities (correlated_values()
+function--defined only if the NumPy module is available).
+
+- Mathematical expressions involving numbers with uncertainties
+generally return AffineScalarFunc objects, which also print as a value
+with uncertainty. Their most useful attributes and methods are
+described in the documentation for AffineScalarFunc. Note that
+Variable objects are also AffineScalarFunc objects. UFloat is an
+alias for AffineScalarFunc, provided as a convenience: testing whether
+a value carries an uncertainty handled by this module should be done
+with insinstance(my_value, UFloat).
+
+- Mathematically, numbers with uncertainties are, in this package,
+probability distributions. These probabilities are reduced to two
+numbers: a nominal value and an uncertainty. Thus, both variables
+(Variable objects) and the result of mathematical operations
+(AffineScalarFunc objects) contain these two values (respectively in
+their nominal_value attribute and through their std_dev() method).
+
+The uncertainty of a number with uncertainty is simply defined in
+this package as the standard deviation of the underlying probability
+distribution.
+
+The numbers with uncertainties manipulated by this package are assumed
+to have a probability distribution mostly contained around their
+nominal value, in an interval of about the size of their standard
+deviation. This should cover most practical cases. A good choice of
+nominal value for a number with uncertainty is thus the median of its
+probability distribution, the location of highest probability, or the
+average value.
+
+- When manipulating ensembles of numbers, some of which contain
+uncertainties, it can be useful to access the nominal value and
+uncertainty of all numbers in a uniform manner:
+
+ x = ufloat("3+/-0.1")
+ print nominal_value(x) # Prints 3
+ print std_dev(x) # Prints 0.1
+ print nominal_value(3) # Prints 3: nominal_value works on floats
+ print std_dev(3) # Prints 0: std_dev works on floats
+
+- Probability distributions (random variables and calculation results)
+are printed as:
+
+ nominal value +/- standard deviation
+
+but this does not imply any property on the nominal value (beyond the
+fact that the nominal value is normally inside the region of high
+probability density), or that the probability distribution of the
+result is symmetrical (this is rarely strictly the case).
+
+- Linear approximations of functions (around the nominal values) are
+used for the calculation of the standard deviation of mathematical
+expressions with this package.
+
+The calculated standard deviations and nominal values are thus
+meaningful approximations as long as the functions involved have
+precise linear expansions in the region where the probability
+distribution of their variables is the largest. It is therefore
+important that uncertainties be small. Mathematically, this means
+that the linear term of functions around the nominal values of their
+variables should be much larger than the remaining higher-order terms
+over the region of significant probability.
+
+For instance, sin(0+/-0.01) yields a meaningful standard deviation
+since it is quite linear over 0+/-0.01. However, cos(0+/-0.01) yields
+an approximate standard deviation of 0 (because the cosine is not well
+approximated by a line around 0), which might not be precise enough
+for all applications.
+
+- Comparison operations (>, ==, etc.) on numbers with uncertainties
+have a pragmatic semantics, in this package: numbers with
+uncertainties can be used wherever Python numbers are used, most of
+the time with a result identical to the one that would be obtained
+with their nominal value only. However, since the objects defined in
+this module represent probability distributions and not pure numbers,
+comparison operator are interpreted in a specific way.
+
+The result of a comparison operation ("==", ">", etc.) is defined so as
+to be essentially consistent with the requirement that uncertainties
+be small: the value of a comparison operation is True only if the
+operation yields True for all infinitesimal variations of its random
+variables, except, possibly, for an infinitely small number of cases.
+
+Example:
+
+ "x = 3.14; y = 3.14" is such that x == y
+
+but
+
+ x = ufloat((3.14, 0.01))
+ y = ufloat((3.14, 0.01))
+
+is not such that x == y, since x and y are independent random
+variables that almost never give the same value. However, x == x
+still holds.
+
+The boolean value (bool(x), "if x...") of a number with uncertainty x
+is the result of x != 0.
+
+- The uncertainties package is for Python 2.5 and above.
+
+- This package contains tests. They can be run either manually or
+automatically with the nose unit testing framework (nosetests).
+
+(c) 2009-2013 by Eric O. LEBIGOT (EOL) <eric.lebigot at normalesup.org>.
+Please send feature requests, bug reports, or feedback to this address.
+
+Please support future development by donating $5 or more through PayPal!
+
+This software is released under a dual license. (1) The BSD license.
+(2) Any other license, as long as it is obtained from the original
+author.'''
+
+# The idea behind this module is to replace the result of mathematical
+# operations by a local approximation of the defining function. For
+# example, sin(0.2+/-0.01) becomes the affine function
+# (AffineScalarFunc object) whose nominal value is sin(0.2) and
+# whose variations are given by sin(0.2+delta) = 0.98...*delta.
+# Uncertainties can then be calculated by using this local linear
+# approximation of the original function.
+
+from __future__ import division # Many analytical derivatives depend on this
+
+import re
+import math
+from math import sqrt, log # Optimization: no attribute look-up
+import copy
+import warnings
+
+# Numerical version:
+__version_info__ = (1, 9)
+__version__ = '.'.join(map(str, __version_info__))
+
+__author__ = 'Eric O. LEBIGOT (EOL) <eric.lebigot at normalesup.org>'
+
+# Attributes that are always exported (some other attributes are
+# exported only if the NumPy module is available...):
+__all__ = [
+
+ # All sub-modules and packages are not imported by default,
+ # in particular because NumPy might be unavailable.
+ 'ufloat', # Main function: returns a number with uncertainty
+
+ # Uniform access to nominal values and standard deviations:
+ 'nominal_value',
+ 'std_dev',
+
+ # Utility functions (more are exported if NumPy is present):
+ 'covariance_matrix',
+
+ # Class for testing whether an object is a number with
+ # uncertainty. Not usually created by users (except through the
+ # Variable subclass), but possibly manipulated by external code
+ # ['derivatives()' method, etc.].
+ 'UFloat',
+
+ # Wrapper for allowing non-pure-Python function to handle
+ # quantities with uncertainties:
+ 'wrap',
+
+ # The documentation for wrap() indicates that numerical
+ # derivatives are calculated through partial_derivative(). The
+ # user might also want to change the size of the numerical
+ # differentiation step.
+ 'partial_derivative'
+ ]
+
+###############################################################################
+
+def set_doc(doc_string):
+ """
+ Decorator function that sets the docstring to the given text.
+
+ It is useful for functions whose docstring is calculated
+ (including string substitutions).
+ """
+ def set_doc_string(func):
+ func.__doc__ = doc_string
+ return func
+ return set_doc_string
+
+# Some types known to not depend on Variable objects are put in
+# CONSTANT_TYPES. The most common types can be put in front, as this
+# may slightly improve the execution speed.
+CONSTANT_TYPES = (float, int, complex) # , long)
+
+###############################################################################
+# Utility for issuing deprecation warnings
+
+def deprecation(message):
+ '''
+ Warns the user with the given message, by issuing a
+ DeprecationWarning.
+ '''
+ warnings.warn(message, DeprecationWarning, stacklevel=2)
+
+
+###############################################################################
+
+## Definitions that depend on the availability of NumPy:
+
+
+try:
+ import numpy
+except ImportError:
+ pass
+else:
+
+ # NumPy numbers do not depend on Variable objects:
+ CONSTANT_TYPES += (numpy.number,)
+
+ # Entering variables as a block of correlated values. Only available
+ # if NumPy is installed.
+
+ #! It would be possible to dispense with NumPy, but a routine should be
+ # written for obtaining the eigenvectors of a symmetric matrix. See
+ # for instance Numerical Recipes: (1) reduction to tri-diagonal
+ # [Givens or Householder]; (2) QR / QL decomposition.
+
+ def correlated_values(nom_values, covariance_mat, tags=None):
+ """
+ Returns numbers with uncertainties (AffineScalarFunc objects)
+ that correctly reproduce the given covariance matrix, and have
+ the given (float) values as their nominal value.
+
+ The correlated_values_norm() function returns the same result,
+ but takes a correlation matrix instead of a covariance matrix.
+
+ The list of values and the covariance matrix must have the
+ same length, and the matrix must be a square (symmetric) one.
+
+ The numbers with uncertainties returned depend on newly
+ created, independent variables (Variable objects).
+
+ If 'tags' is not None, it must list the tag of each new
+ independent variable.
+
+ nom_values -- sequence with the nominal (real) values of the
+ numbers with uncertainties to be returned.
+
+ covariance_mat -- full covariance matrix of the returned
+ numbers with uncertainties (not the statistical correlation
+ matrix, i.e., not the normalized covariance matrix). For
+ example, the first element of this matrix is the variance of
+ the first returned number with uncertainty.
+ """
+
+ # If no tags were given, we prepare tags for the newly created
+ # variables:
+ if tags is None:
+ tags = (None,) * len(nom_values)
+
+ # The covariance matrix is diagonalized in order to define
+ # the independent variables that model the given values:
+
+ (variances, transform) = numpy.linalg.eigh(covariance_mat)
+
+ # Numerical errors might make some variances negative: we set
+ # them to zero:
+ variances[variances < 0] = 0.
+
+ # Creation of new, independent variables:
+
+ # We use the fact that the eigenvectors in 'transform' are
+ # special: 'transform' is unitary: its inverse is its transpose:
+
+ variables = tuple(
+ # The variables represent "pure" uncertainties:
+ Variable(0, sqrt(variance), tag)
+ for (variance, tag) in zip(variances, tags))
+
+ # Representation of the initial correlated values:
+ values_funcs = tuple(
+ AffineScalarFunc(value, dict(zip(variables, coords)))
+ for (coords, value) in zip(transform, nom_values))
+
+ return values_funcs
+
+ __all__.append('correlated_values')
+
+ def correlated_values_norm(values_with_std_dev, correlation_mat,
+ tags=None):
+ '''
+ Returns correlated values like correlated_values(), but takes
+ instead as input:
+
+ - nominal (float) values along with their standard deviation, and
+
+ - a correlation matrix (i.e. a normalized covariance matrix
+ normalized with individual standard deviations).
+
+ values_with_std_dev -- sequence of (nominal value, standard
+ deviation) pairs. The returned, correlated values have these
+ nominal values and standard deviations.
+
+ correlation_mat -- correlation matrix (i.e. the normalized
+ covariance matrix, a matrix with ones on its diagonal).
+ '''
+
+ (nominal_values, std_devs) = numpy.transpose(values_with_std_dev)
+
+ return correlated_values(
+ nominal_values,
+ correlation_mat*std_devs*std_devs[numpy.newaxis].T,
+ tags)
+
+ __all__.append('correlated_values_norm')
+
+###############################################################################
+
+# Mathematical operations with local approximations (affine scalar
+# functions)
+
+class NotUpcast(Exception):
+ 'Raised when an object cannot be converted to a number with uncertainty'
+
+def to_affine_scalar(x):
+ """
+ Transforms x into a constant affine scalar function
+ (AffineScalarFunc), unless it is already an AffineScalarFunc (in
+ which case x is returned unchanged).
+
+ Raises an exception unless 'x' belongs to some specific classes of
+ objects that are known not to depend on AffineScalarFunc objects
+ (which then cannot be considered as constants).
+ """
+
+ if isinstance(x, AffineScalarFunc):
+ return x
+
+ #! In Python 2.6+, numbers.Number could be used instead, here:
+ if isinstance(x, CONSTANT_TYPES):
+ # No variable => no derivative to define:
+ return AffineScalarFunc(x, {})
+
+ # Case of lists, etc.
+ raise NotUpcast("%s cannot be converted to a number with"
+ " uncertainty" % type(x))
+
+def partial_derivative(f, param_num):
+ """
+ Returns a function that numerically calculates the partial
+ derivative of function f with respect to its argument number
+ param_num.
+
+ The step parameter represents the shift of the parameter used in
+ the numerical approximation.
+ """
+
+ def partial_derivative_of_f(*args, **kws):
+ """
+ Partial derivative, calculated with the (-epsilon, +epsilon)
+ method, which is more precise than the (0, +epsilon) method.
+ """
+ # f_nominal_value = f(*args)
+ param_kw = None
+ if '__param__kw__' in kws:
+ param_kw = kws.pop('__param__kw__')
+ shifted_args = list(args) # Copy, and conversion to a mutable
+ shifted_kws = {}
+ for k, v in kws.items():
+ shifted_kws[k] = v
+ step = 1.e-8
+ if param_kw in shifted_kws:
+ step = step*abs(shifted_kws[param_kw])
+ elif param_num < len(shifted_args):
+ # The step is relative to the parameter being varied, so that
+ # shsifting it does not suffer from finite precision:
+ step = step*abs(shifted_args[param_num])
+
+ if param_kw in shifted_kws:
+ shifted_kws[param_kw] += step
+ elif param_num < len(shifted_args):
+ shifted_args[param_num] += step
+
+ shifted_f_plus = f(*shifted_args, **shifted_kws)
+
+ if param_kw in shifted_kws:
+ shifted_kws[param_kw] -= 2*step
+ elif param_num < len(shifted_args):
+ shifted_args[param_num] -= 2*step
+ shifted_f_minus = f(*shifted_args, **shifted_kws)
+
+ return (shifted_f_plus - shifted_f_minus)/2/step
+
+ return partial_derivative_of_f
+
+class NumericalDerivatives(object):
+ """
+ Convenient access to the partial derivatives of a function,
+ calculated numerically.
+ """
+ # This is not a list because the number of arguments of the
+ # function is not known in advance, in general.
+
+ def __init__(self, function):
+ """
+ 'function' is the function whose derivatives can be computed.
+ """
+ self._function = function
+
+ def __getitem__(self, n):
+ """
+ Returns the n-th numerical derivative of the function.
+ """
+ return partial_derivative(self._function, n)
+
+def wrap(f, derivatives_iter=None):
+ """
+ Wraps a function f into a function that also accepts numbers with
+ uncertainties (UFloat objects) and returns a number with
+ uncertainties. Doing so may be necessary when function f cannot
+ be expressed analytically (with uncertainties-compatible operators
+ and functions like +, *, umath.sin(), etc.).
+
+ f must return a scalar (not a list, etc.).
+
+ In the wrapped function, the standard Python scalar arguments of f
+ (float, int, etc.) can be replaced by numbers with
+ uncertainties. The result will contain the appropriate
+ uncertainty.
+
+ If no argument to the wrapped function has an uncertainty, f
+ simply returns its usual, scalar result.
+
+ If supplied, derivatives_iter can be an iterable that generally
+ contains functions; each successive function is the partial
+ derivative of f with respect to the corresponding variable (one
+ function for each argument of f, which takes as many arguments as
+ f). If instead of a function, an element of derivatives_iter
+ contains None, then it is automatically replaced by the relevant
+ numerical derivative; this can be used for non-scalar arguments of
+ f (like string arguments).
+
+ If derivatives_iter is None, or if derivatives_iter contains a
+ fixed (and finite) number of elements, then any missing derivative
+ is calculated numerically.
+
+ An infinite number of derivatives can be specified by having
+ derivatives_iter be an infinite iterator; this can for instance
+ be used for specifying the derivatives of functions with a
+ undefined number of argument (like sum(), whose partial
+ derivatives all return 1).
+
+ Example (for illustration purposes only, as
+ uncertainties.umath.sin() runs faster than the examples that
+ follow): wrap(math.sin) is a sine function that can be applied to
+ numbers with uncertainties. Its derivative will be calculated
+ numerically. wrap(math.sin, [None]) would have produced the same
+ result. wrap(math.sin, [math.cos]) is the same function, but with
+ an analytically defined derivative.
+ """
+
+ if derivatives_iter is None:
+ derivatives_iter = NumericalDerivatives(f)
+ else:
+ # Derivatives that are not defined are calculated numerically,
+ # if there is a finite number of them (the function lambda
+ # *args: fsum(args) has a non-defined number of arguments, as
+ # it just performs a sum):
+ try: # Is the number of derivatives fixed?
+ len(derivatives_iter)
+ except TypeError:
+ pass
+ else:
+ derivatives_iter = [
+ partial_derivative(f, k) if derivative is None
+ else derivative
+ for (k, derivative) in enumerate(derivatives_iter)]
+
+ #! Setting the doc string after "def f_with...()" does not
+ # seem to work. We define it explicitly:
+ @set_doc("""\
+ Version of %s(...) that returns an affine approximation
+ (AffineScalarFunc object), if its result depends on variables
+ (Variable objects). Otherwise, returns a simple constant (when
+ applied to constant arguments).
+
+ Warning: arguments of the function that are not AffineScalarFunc
+ objects must not depend on uncertainties.Variable objects in any
+ way. Otherwise, the dependence of the result in
+ uncertainties.Variable objects will be incorrect.
+
+ Original documentation:
+ %s""" % (f.__name__, f.__doc__))
+ def f_with_affine_output(*args, **kwargs):
+ # Can this function perform the calculation of an
+ # AffineScalarFunc (or maybe float) result?
+ try:
+ old_funcs = map(to_affine_scalar, args)
+ aff_funcs = [to_affine_scalar(a) for a in args]
+ aff_kws = kwargs
+ aff_varkws = []
+ for key, val in kwargs.items():
+ if isinstance(val, Variable):
+ aff_kws[key] = to_affine_scalar(val)
+ aff_varkws.append(key)
+
+ except NotUpcast:
+
+ # This function does not know how to itself perform
+ # calculations with non-float-like arguments (as they
+ # might for instance be objects whose value really changes
+ # if some Variable objects had different values):
+
+ # Is it clear that we can't delegate the calculation?
+
+ if any(isinstance(arg, AffineScalarFunc) for arg in args):
+ # This situation arises for instance when calculating
+ # AffineScalarFunc(...)*numpy.array(...). In this
+ # case, we must let NumPy handle the multiplication
+ # (which is then performed element by element):
+ return NotImplemented
+ else:
+ # If none of the arguments is an AffineScalarFunc, we
+ # can delegate the calculation to the original
+ # function. This can be useful when it is called with
+ # only one argument (as in
+ # numpy.log10(numpy.ndarray(...)):
+ return f(*args, **kwargs)
+
+ ########################################
+ # Nominal value of the constructed AffineScalarFunc:
+ args_values = [e.nominal_value for e in aff_funcs]
+ kw_values = {}
+ for key, val in aff_kws.items():
+ kw_values[key] = val
+ if key in aff_varkws:
+ kw_values[key] = val.nominal_value
+ f_nominal_value = f(*args_values, **kw_values)
+
+ ########################################
+
+ # List of involved variables (Variable objects):
+ variables = set()
+ for expr in aff_funcs:
+ variables |= set(expr.derivatives)
+ for vname in aff_varkws:
+ variables |= set(aff_kws[vname].derivatives)
+ ## It is sometimes useful to only return a regular constant:
+
+ # (1) Optimization / convenience behavior: when 'f' is called
+ # on purely constant values (e.g., sin(2)), there is no need
+ # for returning a more complex AffineScalarFunc object.
+
+ # (2) Functions that do not return a "float-like" value might
+ # not have a relevant representation as an AffineScalarFunc.
+ # This includes boolean functions, since their derivatives are
+ # either 0 or are undefined: they are better represented as
+ # Python constants than as constant AffineScalarFunc functions.
+
+ if not variables or isinstance(f_nominal_value, bool):
+ return f_nominal_value
+
+ # The result of 'f' does depend on 'variables'...
+
+ ########################################
+
+ # Calculation of the derivatives with respect to the arguments
+ # of f (aff_funcs):
+
+ # The chain rule is applied. This is because, in the case of
+ # numerical derivatives, it allows for a better-controlled
+ # numerical stability than numerically calculating the partial
+ # derivatives through '[f(x + dx, y + dy, ...) -
+ # f(x,y,...)]/da' where dx, dy,... are calculated by varying
+ # 'a'. In fact, it is numerically better to control how big
+ # (dx, dy,...) are: 'f' is a simple mathematical function and
+ # it is possible to know how precise the df/dx are (which is
+ # not possible with the numerical df/da calculation above).
+
+ # We use numerical derivatives, if we don't already have a
+ # list of derivatives:
+
+ #! Note that this test could be avoided by requiring the
+ # caller to always provide derivatives. When changing the
+ # functions of the math module, this would force this module
+ # to know about all the math functions. Another possibility
+ # would be to force derivatives_iter to contain, say, the
+ # first 3 derivatives of f. But any of these two ideas has a
+ # chance to break, one day... (if new functions are added to
+ # the math module, or if some function has more than 3
+ # arguments).
+
+ derivatives_wrt_args = []
+ for (arg, derivative) in zip(aff_funcs, derivatives_iter):
+ derivatives_wrt_args.append(derivative(*args_values, **aff_kws)
+ if arg.derivatives
+ else 0)
+
+
+ kws_values = []
+ for vname in aff_varkws:
+ kws_values.append( aff_kws[vname].nominal_value)
+ for (vname, derivative) in zip(aff_varkws, derivatives_iter):
+ derivatives_wrt_args.append(derivative(__param__kw__=vname,
+ **kw_values)
+ if aff_kws[vname].derivatives
+ else 0)
+
+ ########################################
+ # Calculation of the derivative of f with respect to all the
+ # variables (Variable) involved.
+
+ # Initial value (is updated below):
+ derivatives_wrt_vars = dict((var, 0.) for var in variables)
+
+ # The chain rule is used (we already have
+ # derivatives_wrt_args):
+
+ for (func, f_derivative) in zip(aff_funcs, derivatives_wrt_args):
+ for (var, func_derivative) in func.derivatives.items():
+ derivatives_wrt_vars[var] += f_derivative * func_derivative
+
+ for (vname, f_derivative) in zip(aff_varkws, derivatives_wrt_args):
+ func = aff_kws[vname]
+ for (var, func_derivative) in func.derivatives.items():
+ derivatives_wrt_vars[var] += f_derivative * func_derivative
+
+ # The function now returns an AffineScalarFunc object:
+ return AffineScalarFunc(f_nominal_value, derivatives_wrt_vars)
+
+ # It is easier to work with f_with_affine_output, which represents
+ # a wrapped version of 'f', when it bears the same name as 'f':
+ f_with_affine_output.__name__ = f.__name__
+
+ return f_with_affine_output
+
+def _force_aff_func_args(func):
+ """
+ Takes an operator op(x, y) and wraps it.
+
+ The constructed operator returns func(x, to_affine_scalar(y)) if y
+ can be upcast with to_affine_scalar(); otherwise, it returns
+ NotImplemented.
+
+ Thus, func() is only called on two AffineScalarFunc objects, if
+ its first argument is an AffineScalarFunc.
+ """
+
+ def op_on_upcast_args(x, y):
+ """
+ Returns %s(self, to_affine_scalar(y)) if y can be upcast
+ through to_affine_scalar. Otherwise returns NotImplemented.
+ """ % func.__name__
+
+ try:
+ y_with_uncert = to_affine_scalar(y)
+ except NotUpcast:
+ # This module does not know how to handle the comparison:
+ # (example: y is a NumPy array, in which case the NumPy
+ # array will decide that func() should be applied
+ # element-wise between x and all the elements of y):
+ return NotImplemented
+ else:
+ return func(x, y_with_uncert)
+
+ return op_on_upcast_args
+
+########################################
+
+# Definition of boolean operators, that assume that self and
+# y_with_uncert are AffineScalarFunc.
+
+# The fact that uncertainties must be smalled is used, here: the
+# comparison functions are supposed to be constant for most values of
+# the random variables.
+
+# Even though uncertainties are supposed to be small, comparisons
+# between 3+/-0.1 and 3.0 are handled (even though x == 3.0 is not a
+# constant function in the 3+/-0.1 interval). The comparison between
+# x and x is handled too, when x has an uncertainty. In fact, as
+# explained in the main documentation, it is possible to give a useful
+# meaning to the comparison operators, in these cases.
+
+def _eq_on_aff_funcs(self, y_with_uncert):
+ """
+ __eq__ operator, assuming that both self and y_with_uncert are
+ AffineScalarFunc objects.
+ """
+ difference = self - y_with_uncert
+ # Only an exact zero difference means that self and y are
+ # equal numerically:
+ return not(difference._nominal_value or difference.std_dev())
+
+def _ne_on_aff_funcs(self, y_with_uncert):
+ """
+ __ne__ operator, assuming that both self and y_with_uncert are
+ AffineScalarFunc objects.
+ """
+
+ return not _eq_on_aff_funcs(self, y_with_uncert)
+
+def _gt_on_aff_funcs(self, y_with_uncert):
+ """
+ __gt__ operator, assuming that both self and y_with_uncert are
+ AffineScalarFunc objects.
+ """
+ return self._nominal_value > y_with_uncert._nominal_value
+
+def _ge_on_aff_funcs(self, y_with_uncert):
+ """
+ __ge__ operator, assuming that both self and y_with_uncert are
+ AffineScalarFunc objects.
+ """
+
+ return (_gt_on_aff_funcs(self, y_with_uncert)
+ or _eq_on_aff_funcs(self, y_with_uncert))
+
+def _lt_on_aff_funcs(self, y_with_uncert):
+ """
+ __lt__ operator, assuming that both self and y_with_uncert are
+ AffineScalarFunc objects.
+ """
+ return self._nominal_value < y_with_uncert._nominal_value
+
+def _le_on_aff_funcs(self, y_with_uncert):
+ """
+ __le__ operator, assuming that both self and y_with_uncert are
+ AffineScalarFunc objects.
+ """
+
+ return (_lt_on_aff_funcs(self, y_with_uncert)
+ or _eq_on_aff_funcs(self, y_with_uncert))
+
+########################################
+
+class AffineScalarFunc(object):
+ """
+ Affine functions that support basic mathematical operations
+ (addition, etc.). Such functions can for instance be used for
+ representing the local (linear) behavior of any function.
+
+ This class is mostly meant to be used internally.
+
+ This class can also be used to represent constants.
+
+ The variables of affine scalar functions are Variable objects.
+
+ AffineScalarFunc objects include facilities for calculating the
+ 'error' on the function, from the uncertainties on its variables.
+
+ Main attributes and methods:
+
+ - nominal_value, std_dev(): value at the origin / nominal value,
+ and standard deviation.
+
+ - error_components(): error_components()[x] is the error due to
+ Variable x.
+
+ - derivatives: derivatives[x] is the (value of the) derivative
+ with respect to Variable x. This attribute is a dictionary
+ whose keys are the Variable objects on which the function
+ depends.
+
+ All the Variable objects on which the function depends are in
+ 'derivatives'.
+
+ - std_score(x): position of number x with respect to the
+ nominal value, in units of the standard deviation.
+ """
+
+ # To save memory in large arrays:
+ __slots__ = ('_nominal_value', 'derivatives')
+
+ #! The code could be modify in order to accommodate for non-float
+ # nominal values. This could for instance be done through
+ # the operator module: instead of delegating operations to
+ # float.__*__ operations, they could be delegated to
+ # operator.__*__ functions (while taking care of properly handling
+ # reverse operations: __radd__, etc.).
+
+ def __init__(self, nominal_value, derivatives):
+ """
+ nominal_value -- value of the function at the origin.
+ nominal_value must not depend in any way of the Variable
+ objects in 'derivatives' (the value at the origin of the
+ function being defined is a constant).
+
+ derivatives -- maps each Variable object on which the function
+ being defined depends to the value of the derivative with
+ respect to that variable, taken at the nominal value of all
+ variables.
+
+ Warning: the above constraint is not checked, and the user is
+ responsible for complying with it.
+ """
+
+ # Defines the value at the origin:
+
+ # Only float-like values are handled. One reason is that it
+ # does not make sense for a scalar function to be affine to
+ # not yield float values. Another reason is that it would not
+ # make sense to have a complex nominal value, here (it would
+ # not be handled correctly at all): converting to float should
+ # be possible.
+ self._nominal_value = float(nominal_value)
+ self.derivatives = derivatives
+
+ # The following prevents the 'nominal_value' attribute from being
+ # modified by the user:
+ @property
+ def nominal_value(self):
+ "Nominal value of the random number."
+ return self._nominal_value
+
+ ############################################################
+
+
+ ### Operators: operators applied to AffineScalarFunc and/or
+ ### float-like objects only are supported. This is why methods
+ ### from float are used for implementing these operators.
+
+ # Operators with no reflection:
+
+ ########################################
+
+ # __nonzero__() is supposed to return a boolean value (it is used
+ # by bool()). It is for instance used for converting the result
+ # of comparison operators to a boolean, in sorted(). If we want
+ # to be able to sort AffineScalarFunc objects, __nonzero__ cannot
+ # return a AffineScalarFunc object. Since boolean results (such
+ # as the result of bool()) don't have a very meaningful
+ # uncertainty unless it is zero, this behavior is fine.
+
+ def __nonzero__(self):
+ """
+ Equivalent to self != 0.
+ """
+ #! This might not be relevant for AffineScalarFunc objects
+ # that contain values in a linear space which does not convert
+ # the float 0 into the null vector (see the __eq__ function:
+ # __nonzero__ works fine if subtracting the 0 float from a
+ # vector of the linear space works as if 0 were the null
+ # vector of that space):
+ return self != 0. # Uses the AffineScalarFunc.__ne__ function
+
+ ########################################
+
+ ## Logical operators: warning: the resulting value cannot always
+ ## be differentiated.
+
+ # The boolean operations are not differentiable everywhere, but
+ # almost...
+
+ # (1) I can rely on the assumption that the user only has "small"
+ # errors on variables, as this is used in the calculation of the
+ # standard deviation (which performs linear approximations):
+
+ # (2) However, this assumption is not relevant for some
+ # operations, and does not have to hold, in some cases. This
+ # comes from the fact that logical operations (e.g. __eq__(x,y))
+ # are not differentiable for many usual cases. For instance, it
+ # is desirable to have x == x for x = n+/-e, whatever the size of e.
+ # Furthermore, n+/-e != n+/-e', if e != e', whatever the size of e or
+ # e'.
+
+ # (3) The result of logical operators does not have to be a
+ # function with derivatives, as these derivatives are either 0 or
+ # don't exist (i.e., the user should probably not rely on
+ # derivatives for his code).
+
+ # __eq__ is used in "if data in [None, ()]", for instance. It is
+ # therefore important to be able to handle this case too, which is
+ # taken care of when _force_aff_func_args(_eq_on_aff_funcs)
+ # returns NotImplemented.
+ __eq__ = _force_aff_func_args(_eq_on_aff_funcs)
+
+ __ne__ = _force_aff_func_args(_ne_on_aff_funcs)
+ __gt__ = _force_aff_func_args(_gt_on_aff_funcs)
+
+ # __ge__ is not the opposite of __lt__ because these operators do
+ # not always yield a boolean (for instance, 0 <= numpy.arange(10)
+ # yields an array).
+ __ge__ = _force_aff_func_args(_ge_on_aff_funcs)
+
+ __lt__ = _force_aff_func_args(_lt_on_aff_funcs)
+ __le__ = _force_aff_func_args(_le_on_aff_funcs)
+
+ ########################################
+
+ # Uncertainties handling:
+
+ def error_components(self):
+ """
+ Individual components of the standard deviation of the affine
+ function (in absolute value), returned as a dictionary with
+ Variable objects as keys.
+
+ This method assumes that the derivatives contained in the
+ object take scalar values (and are not a tuple, like what
+ math.frexp() returns, for instance).
+ """
+
+ # Calculation of the variance:
+ error_components = {}
+ for (variable, derivative) in self.derivatives.items():
+ # Individual standard error due to variable:
+ error_components[variable] = abs(derivative*variable._std_dev)
+
+ return error_components
+
+ def std_dev(self):
+ """
+ Standard deviation of the affine function.
+
+ This method assumes that the function returns scalar results.
+
+ This returned standard deviation depends on the current
+ standard deviations [std_dev()] of the variables (Variable
+ objects) involved.
+ """
+ #! It would be possible to not allow the user to update the
+ #std dev of Variable objects, in which case AffineScalarFunc
+ #objects could have a pre-calculated or, better, cached
+ #std_dev value (in fact, many intermediate AffineScalarFunc do
+ #not need to have their std_dev calculated: only the final
+ #AffineScalarFunc returned to the user does).
+ return sqrt(sum(
+ delta**2 for delta in self.error_components().values()))
+
+ def _general_representation(self, to_string):
+ """
+ Uses the to_string() conversion function on both the nominal
+ value and the standard deviation, and returns a string that
+ describes them.
+
+ to_string() is typically repr() or str().
+ """
+
+ (nominal_value, std_dev) = (self._nominal_value, self.std_dev())
+
+ # String representation:
+
+ # Not putting spaces around "+/-" helps with arrays of
+ # Variable, as each value with an uncertainty is a
+ # block of signs (otherwise, the standard deviation can be
+ # mistaken for another element of the array).
+
+ return ("%s+/-%s" % (to_string(nominal_value), to_string(std_dev))
+ if std_dev
+ else to_string(nominal_value))
+
+ def __repr__(self):
+ return self._general_representation(repr)
+
+ def __str__(self):
+ return self._general_representation(str)
+
+ def std_score(self, value):
+ """
+ Returns 'value' - nominal value, in units of the standard
+ deviation.
+
+ Raises a ValueError exception if the standard deviation is zero.
+ """
+ try:
+ # The ._nominal_value is a float: there is no integer division,
+ # here:
+ return (value - self._nominal_value) / self.std_dev()
+ except ZeroDivisionError:
+ raise ValueError("The standard deviation is zero:"
+ " undefined result.")
+
+ def __deepcopy__(self, memo):
+ """
+ Hook for the standard copy module.
+
+ The returned AffineScalarFunc is a completely fresh copy,
+ which is fully independent of any variable defined so far.
+ New variables are specially created for the returned
+ AffineScalarFunc object.
+ """
+ return AffineScalarFunc(
+ self._nominal_value,
+ dict((copy.deepcopy(var), deriv)
+ for (var, deriv) in self.derivatives.items()))
+
+ def __getstate__(self):
+ """
+ Hook for the pickle module.
+ """
+ obj_slot_values = dict((k, getattr(self, k)) for k in
+ # self.__slots__ would not work when
+ # self is an instance of a subclass:
+ AffineScalarFunc.__slots__)
+ return obj_slot_values
+
+ def __setstate__(self, data_dict):
+ """
+ Hook for the pickle module.
+ """
+ for (name, value) in data_dict.items():
+ setattr(self, name, value)
+
+# Nicer name, for users: isinstance(ufloat(...), UFloat) is True:
+UFloat = AffineScalarFunc
+
+def get_ops_with_reflection():
+
+ """
+ Returns operators with a reflection, along with their derivatives
+ (for float operands).
+ """
+
+ # Operators with a reflection:
+
+ # We do not include divmod(). This operator could be included, by
+ # allowing its result (a tuple) to be differentiated, in
+ # derivative_value(). However, a similar result can be achieved
+ # by the user by calculating separately the division and the
+ # result.
+
+ # {operator(x, y): (derivative wrt x, derivative wrt y)}:
+
+ # Note that unknown partial derivatives can be numerically
+ # calculated by expressing them as something like
+ # "partial_derivative(float.__...__, 1)(x, y)":
+
+ # String expressions are used, so that reversed operators are easy
+ # to code, and execute relatively efficiently:
+
+ derivatives_list = {
+ 'add': ("1.", "1."),
+ # 'div' is the '/' operator when __future__.division is not in
+ # effect. Since '/' is applied to
+ # AffineScalarFunc._nominal_value numbers, it is applied on
+ # floats, and is therefore the "usual" mathematical division.
+ 'div': ("1/y", "-x/y**2"),
+ 'floordiv': ("0.", "0."), # Non exact: there is a discontinuities
+ # The derivative wrt the 2nd arguments is something like (..., x//y),
+ # but it is calculated numerically, for convenience:
+ 'mod': ("1.", "partial_derivative(float.__mod__, 1)(x, y)"),
+ 'mul': ("y", "x"),
+ 'pow': ("y*x**(y-1)", "log(x)*x**y"),
+ 'sub': ("1.", "-1."),
+ 'truediv': ("1/y", "-x/y**2")
+ }
+
+ # Conversion to Python functions:
+ ops_with_reflection = {}
+ for (op, derivatives) in derivatives_list.items():
+ ops_with_reflection[op] = [
+ eval("lambda x, y: %s" % expr) for expr in derivatives ]
+
+ ops_with_reflection["r"+op] = [
+ eval("lambda y, x: %s" % expr) for expr in reversed(derivatives)]
+
+ return ops_with_reflection
+
+# Operators that have a reflection, along with their derivatives:
+_ops_with_reflection = get_ops_with_reflection()
+
+# Some effectively modified operators (for the automated tests):
+_modified_operators = []
+_modified_ops_with_reflection = []
+
+def add_operators_to_AffineScalarFunc():
+ """
+ Adds many operators (__add__, etc.) to the AffineScalarFunc class.
+ """
+
+ ########################################
+
+ #! Derivatives are set to return floats. For one thing,
+ # uncertainties generally involve floats, as they are based on
+ # small variations of the parameters. It is also better to
+ # protect the user from unexpected integer result that behave
+ # badly with the division.
+
+ ## Operators that return a numerical value:
+
+ # Single-argument operators that should be adapted from floats to
+ # AffineScalarFunc objects, associated to their derivative:
+ simple_numerical_operators_derivatives = {
+ 'abs': lambda x: 1. if x>=0 else -1.,
+ 'neg': lambda x: -1.,
+ 'pos': lambda x: 1.,
+ 'trunc': lambda x: 0.
+ }
+
+ for (op, derivative) in (
+ simple_numerical_operators_derivatives.items()):
+
+ attribute_name = "__%s__" % op
+ # float objects don't exactly have the same attributes between
+ # different versions of Python (for instance, __trunc__ was
+ # introduced with Python 2.6):
+ try:
+ setattr(AffineScalarFunc, attribute_name,
+ wrap(getattr(float, attribute_name),
+ [derivative]))
+ except AttributeError:
+ pass
+ else:
+ _modified_operators.append(op)
+
+ ########################################
+
+ # Reversed versions (useful for float*AffineScalarFunc, for instance):
+ for (op, derivatives) in _ops_with_reflection.items():
+ attribute_name = '__%s__' % op
+ # float objects don't exactly have the same attributes between
+ # different versions of Python (for instance, __div__ and
+ # __rdiv__ were removed, in Python 3):
+ try:
+ setattr(AffineScalarFunc, attribute_name,
+ wrap(getattr(float, attribute_name), derivatives))
+ except AttributeError:
+ pass
+ else:
+ _modified_ops_with_reflection.append(op)
+
+ ########################################
+ # Conversions to pure numbers are meaningless. Note that the
+ # behavior of float(1j) is similar.
+ for coercion_type in ('complex', 'int', 'long', 'float'):
+ def raise_error(self):
+ raise TypeError("can't convert an affine function (%s)"
+ ' to %s; use x.nominal_value'
+ # In case AffineScalarFunc is sub-classed:
+ % (self.__class__, coercion_type))
+
+ setattr(AffineScalarFunc, '__%s__' % coercion_type, raise_error)
+
+add_operators_to_AffineScalarFunc() # Actual addition of class attributes
+
+class Variable(AffineScalarFunc):
+ """
+ Representation of a float-like scalar random variable, along with
+ its uncertainty.
+
+ Objects are meant to represent variables that are independent from
+ each other (correlations are handled through the AffineScalarFunc
+ class).
+ """
+
+ # To save memory in large arrays:
+ __slots__ = ('_std_dev', 'tag')
+
+ def __init__(self, value, std_dev, tag=None):
+ """
+ The nominal value and the standard deviation of the variable
+ are set. These values must be scalars.
+
+ 'tag' is a tag that the user can associate to the variable. This
+ is useful for tracing variables.
+
+ The meaning of the nominal value is described in the main
+ module documentation.
+ """
+
+ #! The value, std_dev, and tag are assumed by __copy__() not to
+ # be copied. Either this should be guaranteed here, or __copy__
+ # should be updated.
+
+ # Only float-like values are handled. One reason is that the
+ # division operator on integers would not produce a
+ # differentiable functions: for instance, Variable(3, 0.1)/2
+ # has a nominal value of 3/2 = 1, but a "shifted" value
+ # of 3.1/2 = 1.55.
+ value = float(value)
+
+ # If the variable changes by dx, then the value of the affine
+ # function that gives its value changes by 1*dx:
+
+ # ! Memory cycles are created. However, they are garbage
+ # collected, if possible. Using a weakref.WeakKeyDictionary
+ # takes much more memory. Thus, this implementation chooses
+ # more cycles and a smaller memory footprint instead of no
+ # cycles and a larger memory footprint.
+
+ # ! Using AffineScalarFunc instead of super() results only in
+ # a 3 % speed loss (Python 2.6, Mac OS X):
+ super(Variable, self).__init__(value, {self: 1.})
+
+ # We force the error to be float-like. Since it is considered
+ # as a Gaussian standard deviation, it is semantically
+ # positive (even though there would be no problem defining it
+ # as a sigma, where sigma can be negative and still define a
+ # Gaussian):
+
+ assert std_dev >= 0, "the error must be a positive number"
+ # Since AffineScalarFunc.std_dev is a property, we cannot do
+ # "self.std_dev = ...":
+ self._std_dev = std_dev
+
+ self.tag = tag
+
+ # Standard deviations can be modified (this is a feature).
+ # AffineScalarFunc objects that depend on the Variable have their
+ # std_dev() automatically modified (recalculated with the new
+ # std_dev of their Variables):
+ def set_std_dev(self, value):
+ """
+ Updates the standard deviation of the variable to a new value.
+ """
+
+ # A zero variance is accepted. Thus, it is possible to
+ # conveniently use infinitely precise variables, for instance
+ # to study special cases.
+
+ self._std_dev = value
+
+ # The following method is overridden so that we can represent the tag:
+ def _general_representation(self, to_string):
+ """
+ Uses the to_string() conversion function on both the nominal
+ value and standard deviation and returns a string that
+ describes the number.
+
+ to_string() is typically repr() or str().
+ """
+ num_repr = super(Variable, self)._general_representation(to_string)
+
+ # Optional tag: only full representations (to_string == repr)
+ # contain the tag, as the tag is required in order to recreate
+ # the variable. Outputting the tag for regular string ("print
+ # x") would be too heavy and produce an unusual representation
+ # of a number with uncertainty.
+ return (num_repr if ((self.tag is None) or (to_string != repr))
+ else "< %s = %s >" % (self.tag, num_repr))
+
+ def __hash__(self):
+ # All Variable objects are by definition independent
+ # variables, so they never compare equal; therefore, their
+ # id() are therefore allowed to differ
+ # (http://docs.python.org/reference/datamodel.html#object.__hash__):
+ return id(self)
+
+ def __copy__(self):
+ """
+ Hook for the standard copy module.
+ """
+
+ # This copy implicitly takes care of the reference of the
+ # variable to itself (in self.derivatives): the new Variable
+ # object points to itself, not to the original Variable.
+
+ # Reference: http://www.doughellmann.com/PyMOTW/copy/index.html
+
+ #! The following assumes that the arguments to Variable are
+ # *not* copied upon construction, since __copy__ is not supposed
+ # to copy "inside" information:
+ return Variable(self.nominal_value, self.std_dev(), self.tag)
+
+ def __deepcopy__(self, memo):
+ """
+ Hook for the standard copy module.
+
+ A new variable is created.
+ """
+
+ # This deep copy implicitly takes care of the reference of the
+ # variable to itself (in self.derivatives): the new Variable
+ # object points to itself, not to the original Variable.
+
+ # Reference: http://www.doughellmann.com/PyMOTW/copy/index.html
+
+ return self.__copy__()
+
+ def __getstate__(self):
+ """
+ Hook for the standard pickle module.
+ """
+ obj_slot_values = dict((k, getattr(self, k)) for k in self.__slots__)
+ obj_slot_values.update(AffineScalarFunc.__getstate__(self))
+ # Conversion to a usual dictionary:
+ return obj_slot_values
+
+ def __setstate__(self, data_dict):
+ """
+ Hook for the standard pickle module.
+ """
+ for (name, value) in data_dict.items():
+ setattr(self, name, value)
+
+###############################################################################
+
+# Utilities
+
+def nominal_value(x):
+ """
+ Returns the nominal value of x if it is a quantity with
+ uncertainty (i.e., an AffineScalarFunc object); otherwise, returns
+ x unchanged.
+
+ This utility function is useful for transforming a series of
+ numbers, when only some of them generally carry an uncertainty.
+ """
+
+ return x.nominal_value if isinstance(x, AffineScalarFunc) else x
+
+def std_dev(x):
+ """
+ Returns the standard deviation of x if it is a quantity with
+ uncertainty (i.e., an AffineScalarFunc object); otherwise, returns
+ the float 0.
+
+ This utility function is useful for transforming a series of
+ numbers, when only some of them generally carry an uncertainty.
+ """
+
+ return x.std_dev() if isinstance(x, AffineScalarFunc) else 0.
+
+def covariance_matrix(nums_with_uncert):
+ """
+ Returns a matrix that contains the covariances between the given
+ sequence of numbers with uncertainties (AffineScalarFunc objects).
+ The resulting matrix implicitly depends on their ordering in
+ 'nums_with_uncert'.
+
+ The covariances are floats (never int objects).
+
+ The returned covariance matrix is the exact linear approximation
+ result, if the nominal values of the numbers with uncertainties
+ and of their variables are their mean. Otherwise, the returned
+ covariance matrix should be close to its linear approximation
+ value.
+
+ The returned matrix is a list of lists.
+ """
+ # See PSI.411 in EOL's notes.
+
+ covariance_matrix = []
+ for (i1, expr1) in enumerate(nums_with_uncert):
+ derivatives1 = expr1.derivatives # Optimization
+ vars1 = set(derivatives1)
+ coefs_expr1 = []
+ for (i2, expr2) in enumerate(nums_with_uncert[:i1+1]):
+ derivatives2 = expr2.derivatives # Optimization
+ coef = 0.
+ for var in vars1.intersection(derivatives2):
+ # var is a variable common to both numbers with
+ # uncertainties:
+ coef += (derivatives1[var]*derivatives2[var]*var._std_dev**2)
+ coefs_expr1.append(coef)
+ covariance_matrix.append(coefs_expr1)
+
+ # We symmetrize the matrix:
+ for (i, covariance_coefs) in enumerate(covariance_matrix):
+ covariance_coefs.extend(covariance_matrix[j][i]
+ for j in range(i+1, len(covariance_matrix)))
+
+ return covariance_matrix
+
+try:
+ import numpy
+except ImportError:
+ pass
+else:
+ def correlation_matrix(nums_with_uncert):
+ '''
+ Returns the correlation matrix of the given sequence of
+ numbers with uncertainties, as a NumPy array of floats.
+ '''
+
+ cov_mat = numpy.array(covariance_matrix(nums_with_uncert))
+
+ std_devs = numpy.sqrt(cov_mat.diagonal())
+
+ return cov_mat/std_devs/std_devs[numpy.newaxis].T
+
+ __all__.append('correlation_matrix')
+
+###############################################################################
+# Parsing of values with uncertainties:
+
+POSITIVE_DECIMAL_UNSIGNED = r'(\d+)(\.\d*)?'
+
+# Regexp for a number with uncertainty (e.g., "-1.234(2)e-6"), where the
+# uncertainty is optional (in which case the uncertainty is implicit):
+NUMBER_WITH_UNCERT_RE_STR = '''
+ ([+-])? # Sign
+ %s # Main number
+ (?:\(%s\))? # Optional uncertainty
+ ([eE][+-]?\d+)? # Optional exponent
+ ''' % (POSITIVE_DECIMAL_UNSIGNED, POSITIVE_DECIMAL_UNSIGNED)
+
+NUMBER_WITH_UNCERT_RE = re.compile(
+ "^%s$" % NUMBER_WITH_UNCERT_RE_STR, re.VERBOSE)
+
+def parse_error_in_parentheses(representation):
+ """
+ Returns (value, error) from a string representing a number with
+ uncertainty like 12.34(5), 12.34(142), 12.5(3.4) or 12.3(4.2)e3.
+ If no parenthesis is given, an uncertainty of one on the last
+ digit is assumed.
+
+ Raises ValueError if the string cannot be parsed.
+ """
+
+ match = NUMBER_WITH_UNCERT_RE.search(representation)
+
+ if match:
+ # The 'main' part is the nominal value, with 'int'eger part, and
+ # 'dec'imal part. The 'uncert'ainty is similarly broken into its
+ # integer and decimal parts.
+ (sign, main_int, main_dec, uncert_int, uncert_dec,
+ exponent) = match.groups()
+ else:
+ raise ValueError("Unparsable number representation: '%s'."
+ " Was expecting a string of the form 1.23(4)"
+ " or 1.234" % representation)
+
+ # The value of the number is its nominal value:
+ value = float(''.join((sign or '',
+ main_int,
+ main_dec or '.0',
+ exponent or '')))
+
+ if uncert_int is None:
+ # No uncertainty was found: an uncertainty of 1 on the last
+ # digit is assumed:
+ uncert_int = '1'
+
+ # Do we have a fully explicit uncertainty?
+ if uncert_dec is not None:
+ uncert = float("%s%s" % (uncert_int, uncert_dec or ''))
+ else:
+ # uncert_int represents an uncertainty on the last digits:
+
+ # The number of digits after the period defines the power of
+ # 10 than must be applied to the provided uncertainty:
+ num_digits_after_period = (0 if main_dec is None
+ else len(main_dec)-1)
+ uncert = int(uncert_int)/10**num_digits_after_period
+
+ # We apply the exponent to the uncertainty as well:
+ uncert *= float("1%s" % (exponent or ''))
+
+ return (value, uncert)
+
+
+# The following function is not exposed because it can in effect be
+# obtained by doing x = ufloat(representation) and
+# x.nominal_value and x.std_dev():
+def str_to_number_with_uncert(representation):
+ """
+ Given a string that represents a number with uncertainty, returns the
+ nominal value and the uncertainty.
+
+ The string can be of the form:
+ - 124.5+/-0.15
+ - 124.50(15)
+ - 124.50(123)
+ - 124.5
+
+ When no numerical error is given, an uncertainty of 1 on the last
+ digit is implied.
+
+ Raises ValueError if the string cannot be parsed.
+ """
+
+ try:
+ # Simple form 1234.45+/-1.2:
+ (value, uncert) = representation.split('+/-')
+ except ValueError:
+ # Form with parentheses or no uncertainty:
+ parsed_value = parse_error_in_parentheses(representation)
+ else:
+ try:
+ parsed_value = (float(value), float(uncert))
+ except ValueError:
+ raise ValueError('Cannot parse %s: was expecting a number'
+ ' like 1.23+/-0.1' % representation)
+
+ return parsed_value
+
+def ufloat(representation, tag=None):
+ """
+ Returns a random variable (Variable object).
+
+ Converts the representation of a number into a number with
+ uncertainty (a random variable, defined by a nominal value and
+ a standard deviation).
+
+ The representation can be a (value, standard deviation) sequence,
+ or a string.
+
+ Strings of the form '12.345+/-0.015', '12.345(15)', or '12.3' are
+ recognized (see full list below). In the last case, an
+ uncertainty of +/-1 is assigned to the last digit.
+
+ 'tag' is an optional string tag for the variable. Variables
+ don't have to have distinct tags. Tags are useful for tracing
+ what values (and errors) enter in a given result (through the
+ error_components() method).
+
+ Examples of valid string representations:
+
+ -1.23(3.4)
+ -1.34(5)
+ 1(6)
+ 3(4.2)
+ -9(2)
+ 1234567(1.2)
+ 12.345(15)
+ -12.3456(78)e-6
+ 12.3(0.4)e-5
+ 0.29
+ 31.
+ -31.
+ 31
+ -3.1e10
+ 169.0(7)
+ 169.1(15)
+ """
+
+ # This function is somewhat optimized so as to help with the
+ # creation of lots of Variable objects (through unumpy.uarray, for
+ # instance).
+
+ # representations is "normalized" so as to be a valid sequence of
+ # 2 arguments for Variable().
+
+ #! Accepting strings and any kind of sequence slows down the code
+ # by about 5 %. On the other hand, massive initializations of
+ # numbers with uncertainties are likely to be performed with
+ # unumpy.uarray, which does not support parsing from strings and
+ # thus does not have any overhead.
+
+ #! Different, in Python 3:
+ if isinstance(representation, basestring):
+ representation = str_to_number_with_uncert(representation)
+
+ #! The tag is forced to be a string, so that the user does not
+ # create a Variable(2.5, 0.5) in order to represent 2.5 +/- 0.5.
+ # Forcing 'tag' to be a string prevents numerical uncertainties
+ # from being considered as tags, here:
+ if tag is not None:
+ #! 'unicode' is removed in Python3:
+ assert isinstance(tag, (str, unicode)), "The tag can only be a string."
+
+ #! The special ** syntax is for Python 2.5 and before (Python 2.6+
+ # understands tag=tag):
+ return Variable(*representation, **{'tag': tag})
+
diff --git a/lmfit/uncertainties/umath.py b/lmfit/uncertainties/umath.py
index 5487b63..e0608c8 100644
--- a/lmfit/uncertainties/umath.py
+++ b/lmfit/uncertainties/umath.py
@@ -1,350 +1,350 @@
-'''
-Mathematical operations that generalize many operations from the
-standard math module so that they also work on numbers with
-uncertainties.
-
-Examples:
-
- from umath import sin
-
- # Manipulation of numbers with uncertainties:
- x = uncertainties.ufloat((3, 0.1))
- print sin(x) # prints 0.141120008...+/-0.098999...
-
- # The umath functions also work on regular Python floats:
- print sin(3) # prints 0.141120008... This is a Python float.
-
-Importing all the functions from this module into the global namespace
-is possible. This is encouraged when using a Python shell as a
-calculator. Example:
-
- import uncertainties
- from uncertainties.umath import * # Imports tan(), etc.
-
- x = uncertainties.ufloat((3, 0.1))
- print tan(x) # tan() is the uncertainties.umath.tan function
-
-The numbers with uncertainties handled by this module are objects from
-the uncertainties module, from either the Variable or the
-AffineScalarFunc class.
-
-(c) 2009-2013 by Eric O. LEBIGOT (EOL) <eric.lebigot at normalesup.org>.
-Please send feature requests, bug reports, or feedback to this address.
-
-This software is released under a dual license. (1) The BSD license.
-(2) Any other license, as long as it is obtained from the original
-author.'''
-
-from __future__ import division # Many analytical derivatives depend on this
-
-# Standard modules
-import math
-import sys
-import itertools
-import functools
-
-# Local modules
-from __init__ import wrap, set_doc, __author__, to_affine_scalar, AffineScalarFunc
-
-###############################################################################
-
-# We wrap the functions from the math module so that they keep track of
-# uncertainties by returning a AffineScalarFunc object.
-
-# Some functions from the math module cannot be adapted in a standard
-# way so to work with AffineScalarFunc objects (either as their result
-# or as their arguments):
-
-# (1) Some functions return a result of a type whose value and
-# variations (uncertainties) cannot be represented by AffineScalarFunc
-# (e.g., math.frexp, which returns a tuple). The exception raised
-# when not wrapping them with wrap() is more obvious than the
-# one obtained when wrapping them (in fact, the wrapped functions
-# attempts operations that are not supported, such as calculation a
-# subtraction on a result of type tuple).
-
-# (2) Some functions don't take continuous scalar arguments (which can
-# be varied during differentiation): math.fsum, math.factorial...
-# Such functions can either be:
-
-# - wrapped in a special way.
-
-# - excluded from standard wrapping by adding their name to
-# no_std_wrapping
-
-# Math functions that have a standard interface: they take
-# one or more float arguments, and return a scalar:
-many_scalars_to_scalar_funcs = []
-
-# Some functions require a specific treatment and must therefore be
-# excluded from standard wrapping. Functions
-# no_std_wrapping = ['modf', 'frexp', 'ldexp', 'fsum', 'factorial']
-
-# Functions with numerical derivatives:
-num_deriv_funcs = ['fmod', 'gamma', 'isinf', 'isnan',
- 'lgamma', 'trunc']
-
-# Functions that do not belong in many_scalars_to_scalar_funcs, but
-# that have a version that handles uncertainties:
-non_std_wrapped_funcs = []
-
-# Function that copies the relevant attributes from generalized
-# functions from the math module:
-wraps = functools.partial(functools.update_wrapper,
- assigned=('__doc__', '__name__'))
-
-########################################
-# Wrapping of math functions:
-
-# Fixed formulas for the derivatives of some functions from the math
-# module (some functions might not be present in all version of
-# Python). Singular points are not taken into account. The user
-# should never give "large" uncertainties: problems could only appear
-# if this assumption does not hold.
-
-# Functions not mentioned in _fixed_derivatives have their derivatives
-# calculated numerically.
-
-# Functions that have singularities (possibly at infinity) benefit
-# from analytical calculations (instead of the default numerical
-# calculation) because their derivatives generally change very fast.
-# Even slowly varying functions (e.g., abs()) yield more precise
-# results when differentiated analytically, because of the loss of
-# precision in numerical calculations.
-
-#def log_1arg_der(x):
-# """
-# Derivative of log(x) (1-argument form).
-# """
-# return 1/x
-
-
-def log_der0(*args):
- """
- Derivative of math.log() with respect to its first argument.
-
- Works whether 1 or 2 arguments are given.
- """
- if len(args) == 1:
- return 1/args[0]
- else:
- return 1/args[0]/math.log(args[1]) # 2-argument form
-
- # The following version goes about as fast:
-
- ## A 'try' is used for the most common case because it is fast when no
- ## exception is raised:
- #try:
- # return log_1arg_der(*args) # Argument number check
- #except TypeError:
- # return 1/args[0]/math.log(args[1]) # 2-argument form
-
-_erf_coef = 2/math.sqrt(math.pi) # Optimization for erf()
-
-fixed_derivatives = {
- # In alphabetical order, here:
- 'acos': [lambda x: -1/math.sqrt(1-x**2)],
- 'acosh': [lambda x: 1/math.sqrt(x**2-1)],
- 'asin': [lambda x: 1/math.sqrt(1-x**2)],
- 'asinh': [lambda x: 1/math.sqrt(1+x**2)],
- 'atan': [lambda x: 1/(1+x**2)],
- 'atan2': [lambda y, x: x/(x**2+y**2), # Correct for x == 0
- lambda y, x: -y/(x**2+y**2)], # Correct for x == 0
- 'atanh': [lambda x: 1/(1-x**2)],
- 'ceil': [lambda x: 0],
- 'copysign': [lambda x, y: (1 if x >= 0 else -1) * math.copysign(1, y),
- lambda x, y: 0],
- 'cos': [lambda x: -math.sin(x)],
- 'cosh': [math.sinh],
- 'degrees': [lambda x: math.degrees(1)],
- 'erf': [lambda x: math.exp(-x**2)*_erf_coef],
- 'erfc': [lambda x: -math.exp(-x**2)*_erf_coef],
- 'exp': [math.exp],
- 'expm1': [math.exp],
- 'fabs': [lambda x: 1 if x >= 0 else -1],
- 'floor': [lambda x: 0],
- 'hypot': [lambda x, y: x/math.hypot(x, y),
- lambda x, y: y/math.hypot(x, y)],
- 'log': [log_der0,
- lambda x, y: -math.log(x, y)/y/math.log(y)],
- 'log10': [lambda x: 1/x/math.log(10)],
- 'log1p': [lambda x: 1/(1+x)],
- 'pow': [lambda x, y: y*math.pow(x, y-1),
- lambda x, y: math.log(x) * math.pow(x, y)],
- 'radians': [lambda x: math.radians(1)],
- 'sin': [math.cos],
- 'sinh': [math.cosh],
- 'sqrt': [lambda x: 0.5/math.sqrt(x)],
- 'tan': [lambda x: 1+math.tan(x)**2],
- 'tanh': [lambda x: 1-math.tanh(x)**2]
- }
-
-# Many built-in functions in the math module are wrapped with a
-# version which is uncertainty aware:
-
-this_module = sys.modules[__name__]
-
-# for (name, attr) in vars(math).items():
-for name in dir(math):
-
- if name in fixed_derivatives: # Priority to functions in fixed_derivatives
- derivatives = fixed_derivatives[name]
- elif name in num_deriv_funcs:
- # Functions whose derivatives are calculated numerically by
- # this module fall here (isinf, fmod,...):
- derivatives = None # Means: numerical calculation required
- else:
- continue # 'name' not wrapped by this module (__doc__, e, etc.)
-
- func = getattr(math, name)
-
- setattr(this_module, name,
- wraps(wrap(func, derivatives), func))
-
- many_scalars_to_scalar_funcs.append(name)
-
-###############################################################################
-
-########################################
-# Special cases: some of the functions from no_std_wrapping:
-
-##########
-# The math.factorial function is not converted to an uncertainty-aware
-# function, because it does not handle non-integer arguments: it does
-# not make sense to give it an argument with a numerical error
-# (whereas this would be relevant for the gamma function).
-
-##########
-
-# fsum takes a single argument, which cannot be differentiated.
-# However, each of the arguments inside this single list can
-# be a variable. We handle this in a specific way:
-
-if sys.version_info[:2] >= (2, 6):
-
- # For drop-in compatibility with the math module:
- factorial = math.factorial
- non_std_wrapped_funcs.append('factorial')
-
-
- # We wrap math.fsum
- original_func = math.fsum # For optimization purposes
-
- # The function below exists so that temporary variables do not
- # pollute the module namespace:
- def wrapped_fsum():
- """
- Returns an uncertainty-aware version of math.fsum, which must
- be contained in _original_func.
- """
-
- # The fsum function is flattened, in order to use the
- # wrap() wrapper:
-
- flat_fsum = lambda *args: original_func(args)
-
- flat_fsum_wrap = wrap(
- flat_fsum, itertools.repeat(lambda *args: 1))
-
- return wraps(lambda arg_list: flat_fsum_wrap(*arg_list),
- original_func)
-
- fsum = wrapped_fsum()
- non_std_wrapped_funcs.append('fsum')
-
-
- at set_doc(math.modf.__doc__)
-def modf(x):
- """
- Version of modf that works for numbers with uncertainty, and also
- for regular numbers.
- """
-
- # The code below is inspired by wrap(). It is
- # simpler because only 1 argument is given, and there is no
- # delegation to other functions involved (as for __mul__, etc.).
-
- aff_func = to_affine_scalar(x)
-
- (frac_part, int_part) = math.modf(aff_func.nominal_value)
-
- if aff_func.derivatives:
- # The derivative of the fractional part is simply 1: the
- # derivatives of modf(x)[0] are the derivatives of x:
- return (AffineScalarFunc(frac_part, aff_func.derivatives), int_part)
- else:
- # This function was not called with an AffineScalarFunc
- # argument: there is no need to return numbers with uncertainties:
- return (frac_part, int_part)
-
-many_scalars_to_scalar_funcs.append('modf')
-
-
- at set_doc(math.ldexp.__doc__)
-def ldexp(x, y):
- # The code below is inspired by wrap(). It is
- # simpler because only 1 argument is given, and there is no
- # delegation to other functions involved (as for __mul__, etc.).
-
- # Another approach would be to add an additional argument to
- # wrap() so that some arguments are automatically
- # considered as constants.
-
- aff_func = to_affine_scalar(x) # y must be an integer, for math.ldexp
-
- if aff_func.derivatives:
- factor = 2**y
- return AffineScalarFunc(
- math.ldexp(aff_func.nominal_value, y),
- # Chain rule:
- dict((var, factor*deriv)
- for (var, deriv) in aff_func.derivatives.iteritems()))
- else:
- # This function was not called with an AffineScalarFunc
- # argument: there is no need to return numbers with uncertainties:
-
- # aff_func.nominal_value is not passed instead of x, because
- # we do not have to care about the type of the return value of
- # math.ldexp, this way (aff_func.nominal_value might be the
- # value of x coerced to a difference type [int->float, for
- # instance]):
- return math.ldexp(x, y)
-many_scalars_to_scalar_funcs.append('ldexp')
-
-
- at set_doc(math.frexp.__doc__)
-def frexp(x):
- """
- Version of frexp that works for numbers with uncertainty, and also
- for regular numbers.
- """
-
- # The code below is inspired by wrap(). It is
- # simpler because only 1 argument is given, and there is no
- # delegation to other functions involved (as for __mul__, etc.).
-
- aff_func = to_affine_scalar(x)
-
- if aff_func.derivatives:
- result = math.frexp(aff_func.nominal_value)
- # With frexp(x) = (m, e), dm/dx = 1/(2**e):
- factor = 1/(2**result[1])
- return (
- AffineScalarFunc(
- result[0],
- # Chain rule:
- dict((var, factor*deriv)
- for (var, deriv) in aff_func.derivatives.iteritems())),
- # The exponent is an integer and is supposed to be
- # continuous (small errors):
- result[1])
- else:
- # This function was not called with an AffineScalarFunc
- # argument: there is no need to return numbers with uncertainties:
- return math.frexp(x)
-non_std_wrapped_funcs.append('frexp')
-
-###############################################################################
-# Exported functions:
-
-__all__ = many_scalars_to_scalar_funcs + non_std_wrapped_funcs
+'''
+Mathematical operations that generalize many operations from the
+standard math module so that they also work on numbers with
+uncertainties.
+
+Examples:
+
+ from umath import sin
+
+ # Manipulation of numbers with uncertainties:
+ x = uncertainties.ufloat((3, 0.1))
+ print sin(x) # prints 0.141120008...+/-0.098999...
+
+ # The umath functions also work on regular Python floats:
+ print sin(3) # prints 0.141120008... This is a Python float.
+
+Importing all the functions from this module into the global namespace
+is possible. This is encouraged when using a Python shell as a
+calculator. Example:
+
+ import uncertainties
+ from uncertainties.umath import * # Imports tan(), etc.
+
+ x = uncertainties.ufloat((3, 0.1))
+ print tan(x) # tan() is the uncertainties.umath.tan function
+
+The numbers with uncertainties handled by this module are objects from
+the uncertainties module, from either the Variable or the
+AffineScalarFunc class.
+
+(c) 2009-2013 by Eric O. LEBIGOT (EOL) <eric.lebigot at normalesup.org>.
+Please send feature requests, bug reports, or feedback to this address.
+
+This software is released under a dual license. (1) The BSD license.
+(2) Any other license, as long as it is obtained from the original
+author.'''
+
+from __future__ import division # Many analytical derivatives depend on this
+
+# Standard modules
+import math
+import sys
+import itertools
+import functools
+
+# Local modules
+from __init__ import wrap, set_doc, __author__, to_affine_scalar, AffineScalarFunc
+
+###############################################################################
+
+# We wrap the functions from the math module so that they keep track of
+# uncertainties by returning a AffineScalarFunc object.
+
+# Some functions from the math module cannot be adapted in a standard
+# way so to work with AffineScalarFunc objects (either as their result
+# or as their arguments):
+
+# (1) Some functions return a result of a type whose value and
+# variations (uncertainties) cannot be represented by AffineScalarFunc
+# (e.g., math.frexp, which returns a tuple). The exception raised
+# when not wrapping them with wrap() is more obvious than the
+# one obtained when wrapping them (in fact, the wrapped functions
+# attempts operations that are not supported, such as calculation a
+# subtraction on a result of type tuple).
+
+# (2) Some functions don't take continuous scalar arguments (which can
+# be varied during differentiation): math.fsum, math.factorial...
+# Such functions can either be:
+
+# - wrapped in a special way.
+
+# - excluded from standard wrapping by adding their name to
+# no_std_wrapping
+
+# Math functions that have a standard interface: they take
+# one or more float arguments, and return a scalar:
+many_scalars_to_scalar_funcs = []
+
+# Some functions require a specific treatment and must therefore be
+# excluded from standard wrapping. Functions
+# no_std_wrapping = ['modf', 'frexp', 'ldexp', 'fsum', 'factorial']
+
+# Functions with numerical derivatives:
+num_deriv_funcs = ['fmod', 'gamma', 'isinf', 'isnan',
+ 'lgamma', 'trunc']
+
+# Functions that do not belong in many_scalars_to_scalar_funcs, but
+# that have a version that handles uncertainties:
+non_std_wrapped_funcs = []
+
+# Function that copies the relevant attributes from generalized
+# functions from the math module:
+wraps = functools.partial(functools.update_wrapper,
+ assigned=('__doc__', '__name__'))
+
+########################################
+# Wrapping of math functions:
+
+# Fixed formulas for the derivatives of some functions from the math
+# module (some functions might not be present in all version of
+# Python). Singular points are not taken into account. The user
+# should never give "large" uncertainties: problems could only appear
+# if this assumption does not hold.
+
+# Functions not mentioned in _fixed_derivatives have their derivatives
+# calculated numerically.
+
+# Functions that have singularities (possibly at infinity) benefit
+# from analytical calculations (instead of the default numerical
+# calculation) because their derivatives generally change very fast.
+# Even slowly varying functions (e.g., abs()) yield more precise
+# results when differentiated analytically, because of the loss of
+# precision in numerical calculations.
+
+#def log_1arg_der(x):
+# """
+# Derivative of log(x) (1-argument form).
+# """
+# return 1/x
+
+
+def log_der0(*args):
+ """
+ Derivative of math.log() with respect to its first argument.
+
+ Works whether 1 or 2 arguments are given.
+ """
+ if len(args) == 1:
+ return 1/args[0]
+ else:
+ return 1/args[0]/math.log(args[1]) # 2-argument form
+
+ # The following version goes about as fast:
+
+ ## A 'try' is used for the most common case because it is fast when no
+ ## exception is raised:
+ #try:
+ # return log_1arg_der(*args) # Argument number check
+ #except TypeError:
+ # return 1/args[0]/math.log(args[1]) # 2-argument form
+
+_erf_coef = 2/math.sqrt(math.pi) # Optimization for erf()
+
+fixed_derivatives = {
+ # In alphabetical order, here:
+ 'acos': [lambda x: -1/math.sqrt(1-x**2)],
+ 'acosh': [lambda x: 1/math.sqrt(x**2-1)],
+ 'asin': [lambda x: 1/math.sqrt(1-x**2)],
+ 'asinh': [lambda x: 1/math.sqrt(1+x**2)],
+ 'atan': [lambda x: 1/(1+x**2)],
+ 'atan2': [lambda y, x: x/(x**2+y**2), # Correct for x == 0
+ lambda y, x: -y/(x**2+y**2)], # Correct for x == 0
+ 'atanh': [lambda x: 1/(1-x**2)],
+ 'ceil': [lambda x: 0],
+ 'copysign': [lambda x, y: (1 if x >= 0 else -1) * math.copysign(1, y),
+ lambda x, y: 0],
+ 'cos': [lambda x: -math.sin(x)],
+ 'cosh': [math.sinh],
+ 'degrees': [lambda x: math.degrees(1)],
+ 'erf': [lambda x: math.exp(-x**2)*_erf_coef],
+ 'erfc': [lambda x: -math.exp(-x**2)*_erf_coef],
+ 'exp': [math.exp],
+ 'expm1': [math.exp],
+ 'fabs': [lambda x: 1 if x >= 0 else -1],
+ 'floor': [lambda x: 0],
+ 'hypot': [lambda x, y: x/math.hypot(x, y),
+ lambda x, y: y/math.hypot(x, y)],
+ 'log': [log_der0,
+ lambda x, y: -math.log(x, y)/y/math.log(y)],
+ 'log10': [lambda x: 1/x/math.log(10)],
+ 'log1p': [lambda x: 1/(1+x)],
+ 'pow': [lambda x, y: y*math.pow(x, y-1),
+ lambda x, y: math.log(x) * math.pow(x, y)],
+ 'radians': [lambda x: math.radians(1)],
+ 'sin': [math.cos],
+ 'sinh': [math.cosh],
+ 'sqrt': [lambda x: 0.5/math.sqrt(x)],
+ 'tan': [lambda x: 1+math.tan(x)**2],
+ 'tanh': [lambda x: 1-math.tanh(x)**2]
+ }
+
+# Many built-in functions in the math module are wrapped with a
+# version which is uncertainty aware:
+
+this_module = sys.modules[__name__]
+
+# for (name, attr) in vars(math).items():
+for name in dir(math):
+
+ if name in fixed_derivatives: # Priority to functions in fixed_derivatives
+ derivatives = fixed_derivatives[name]
+ elif name in num_deriv_funcs:
+ # Functions whose derivatives are calculated numerically by
+ # this module fall here (isinf, fmod,...):
+ derivatives = None # Means: numerical calculation required
+ else:
+ continue # 'name' not wrapped by this module (__doc__, e, etc.)
+
+ func = getattr(math, name)
+
+ setattr(this_module, name,
+ wraps(wrap(func, derivatives), func))
+
+ many_scalars_to_scalar_funcs.append(name)
+
+###############################################################################
+
+########################################
+# Special cases: some of the functions from no_std_wrapping:
+
+##########
+# The math.factorial function is not converted to an uncertainty-aware
+# function, because it does not handle non-integer arguments: it does
+# not make sense to give it an argument with a numerical error
+# (whereas this would be relevant for the gamma function).
+
+##########
+
+# fsum takes a single argument, which cannot be differentiated.
+# However, each of the arguments inside this single list can
+# be a variable. We handle this in a specific way:
+
+if sys.version_info[:2] >= (2, 6):
+
+ # For drop-in compatibility with the math module:
+ factorial = math.factorial
+ non_std_wrapped_funcs.append('factorial')
+
+
+ # We wrap math.fsum
+ original_func = math.fsum # For optimization purposes
+
+ # The function below exists so that temporary variables do not
+ # pollute the module namespace:
+ def wrapped_fsum():
+ """
+ Returns an uncertainty-aware version of math.fsum, which must
+ be contained in _original_func.
+ """
+
+ # The fsum function is flattened, in order to use the
+ # wrap() wrapper:
+
+ flat_fsum = lambda *args: original_func(args)
+
+ flat_fsum_wrap = wrap(
+ flat_fsum, itertools.repeat(lambda *args: 1))
+
+ return wraps(lambda arg_list: flat_fsum_wrap(*arg_list),
+ original_func)
+
+ fsum = wrapped_fsum()
+ non_std_wrapped_funcs.append('fsum')
+
+
+ at set_doc(math.modf.__doc__)
+def modf(x):
+ """
+ Version of modf that works for numbers with uncertainty, and also
+ for regular numbers.
+ """
+
+ # The code below is inspired by wrap(). It is
+ # simpler because only 1 argument is given, and there is no
+ # delegation to other functions involved (as for __mul__, etc.).
+
+ aff_func = to_affine_scalar(x)
+
+ (frac_part, int_part) = math.modf(aff_func.nominal_value)
+
+ if aff_func.derivatives:
+ # The derivative of the fractional part is simply 1: the
+ # derivatives of modf(x)[0] are the derivatives of x:
+ return (AffineScalarFunc(frac_part, aff_func.derivatives), int_part)
+ else:
+ # This function was not called with an AffineScalarFunc
+ # argument: there is no need to return numbers with uncertainties:
+ return (frac_part, int_part)
+
+many_scalars_to_scalar_funcs.append('modf')
+
+
+ at set_doc(math.ldexp.__doc__)
+def ldexp(x, y):
+ # The code below is inspired by wrap(). It is
+ # simpler because only 1 argument is given, and there is no
+ # delegation to other functions involved (as for __mul__, etc.).
+
+ # Another approach would be to add an additional argument to
+ # wrap() so that some arguments are automatically
+ # considered as constants.
+
+ aff_func = to_affine_scalar(x) # y must be an integer, for math.ldexp
+
+ if aff_func.derivatives:
+ factor = 2**y
+ return AffineScalarFunc(
+ math.ldexp(aff_func.nominal_value, y),
+ # Chain rule:
+ dict((var, factor*deriv)
+ for (var, deriv) in aff_func.derivatives.iteritems()))
+ else:
+ # This function was not called with an AffineScalarFunc
+ # argument: there is no need to return numbers with uncertainties:
+
+ # aff_func.nominal_value is not passed instead of x, because
+ # we do not have to care about the type of the return value of
+ # math.ldexp, this way (aff_func.nominal_value might be the
+ # value of x coerced to a difference type [int->float, for
+ # instance]):
+ return math.ldexp(x, y)
+many_scalars_to_scalar_funcs.append('ldexp')
+
+
+ at set_doc(math.frexp.__doc__)
+def frexp(x):
+ """
+ Version of frexp that works for numbers with uncertainty, and also
+ for regular numbers.
+ """
+
+ # The code below is inspired by wrap(). It is
+ # simpler because only 1 argument is given, and there is no
+ # delegation to other functions involved (as for __mul__, etc.).
+
+ aff_func = to_affine_scalar(x)
+
+ if aff_func.derivatives:
+ result = math.frexp(aff_func.nominal_value)
+ # With frexp(x) = (m, e), dm/dx = 1/(2**e):
+ factor = 1/(2**result[1])
+ return (
+ AffineScalarFunc(
+ result[0],
+ # Chain rule:
+ dict((var, factor*deriv)
+ for (var, deriv) in aff_func.derivatives.iteritems())),
+ # The exponent is an integer and is supposed to be
+ # continuous (small errors):
+ result[1])
+ else:
+ # This function was not called with an AffineScalarFunc
+ # argument: there is no need to return numbers with uncertainties:
+ return math.frexp(x)
+non_std_wrapped_funcs.append('frexp')
+
+###############################################################################
+# Exported functions:
+
+__all__ = many_scalars_to_scalar_funcs + non_std_wrapped_funcs
diff --git a/publish_docs.sh b/publish_docs.sh
index e3badfe..5ffd2ba 100644
--- a/publish_docs.sh
+++ b/publish_docs.sh
@@ -1,59 +1,59 @@
-installdir='/www/apache/htdocs/software/python/lmfit'
-docbuild='doc/_build'
-
-cd doc
-echo '# Making docs'
-make all
-cd ../
-
-echo '# Building tarball of docs'
-mkdir _tmpdoc
-cp -pr doc/lmfit.pdf _tmpdoc/lmfit.pdf
-cp -pr doc/_build/html/* _tmpdoc/.
-cd _tmpdoc
-tar czf ../../lmfit_docs.tar.gz .
-cd ..
-rm -rf _tmpdoc
-
-#
-echo "# Switching to gh-pages branch"
-git checkout gh-pages
-
-if [ $? -ne 0 ] ; then
- echo ' failed.'
- exit
-fi
-
-tar xzf ../lmfit_docs.tar.gz .
-
-echo "# commit changes to gh-pages branch"
-git commit -am "changed docs"
-
-if [ $? -ne 0 ] ; then
- echo ' failed.'
- exit
-fi
-
-echo "# Pushing docs to github"
-git push
-
-
-echo "# switch back to master branch"
-git checkout master
-
-if [ $? -ne 0 ] ; then
- echo ' failed.'
- exit
-fi
-
-# install locally
-echo "# Installing docs to CARS web pages"
-cp ../lmfit_docs.tar.gz $installdir/..
-
-cd $installdir
-if [ $? -ne 0 ] ; then
- echo ' failed.'
- exit
-fi
-
-tar xvzf ../lmfit_docs.tar.gz
+installdir='/www/apache/htdocs/software/python/lmfit'
+docbuild='doc/_build'
+
+cd doc
+echo '# Making docs'
+make all
+cd ../
+
+echo '# Building tarball of docs'
+mkdir _tmpdoc
+cp -pr doc/lmfit.pdf _tmpdoc/lmfit.pdf
+cp -pr doc/_build/html/* _tmpdoc/.
+cd _tmpdoc
+tar czf ../../lmfit_docs.tar.gz .
+cd ..
+rm -rf _tmpdoc
+
+#
+echo "# Switching to gh-pages branch"
+git checkout gh-pages
+
+if [ $? -ne 0 ] ; then
+ echo ' failed.'
+ exit
+fi
+
+tar xzf ../lmfit_docs.tar.gz .
+
+echo "# commit changes to gh-pages branch"
+git commit -am "changed docs"
+
+if [ $? -ne 0 ] ; then
+ echo ' failed.'
+ exit
+fi
+
+echo "# Pushing docs to github"
+git push
+
+
+echo "# switch back to master branch"
+git checkout master
+
+if [ $? -ne 0 ] ; then
+ echo ' failed.'
+ exit
+fi
+
+# install locally
+echo "# Installing docs to CARS web pages"
+cp ../lmfit_docs.tar.gz $installdir/..
+
+cd $installdir
+if [ $? -ne 0 ] ; then
+ echo ' failed.'
+ exit
+fi
+
+tar xvzf ../lmfit_docs.tar.gz
diff --git a/requirements.txt b/requirements.txt
index fecf23c..fe73b4f 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,2 +1,2 @@
-numpy>=1.5
-scipy>=0.13
+numpy>=1.5
+scipy>=0.13
diff --git a/setup.py b/setup.py
index faa4469..ac98539 100644
--- a/setup.py
+++ b/setup.py
@@ -1,54 +1,54 @@
-#!/usr/bin/env python
-# from distutils.core import setup
-from setuptools import setup
-
-import versioneer
-versioneer.VCS = 'git'
-versioneer.versionfile_source = 'lmfit/_version.py'
-versioneer.versionfile_build = 'lmfit/_version.py'
-versioneer.tag_prefix = ''
-versioneer.parentdir_prefix = 'lmfit-'
-
-
-long_desc = """A library for least-squares minimization and data fitting in
-Python. Built on top of scipy.optimize, lmfit provides a Parameter object
-which can be set as fixed or free, can have upper and/or lower bounds, or
-can be written in terms of algebraic constraints of other Parameters. The
-user writes a function to be minimized as a function of these Parameters,
-and the scipy.optimize methods are used to find the optimal values for the
-Parameters. The Levenberg-Marquardt (leastsq) is the default minimization
-algorithm, and provides estimated standard errors and correlations between
-varied Parameters. Other minimization methods, including Nelder-Mead's
-downhill simplex, Powell's method, BFGS, Sequential Least Squares, and
-others are also supported. Bounds and contraints can be placed on
-Parameters for all of these methods.
-
-In addition, methods for explicitly calculating confidence intervals are
-provided for exploring minmization problems where the approximation of
-estimating Parameter uncertainties from the covariance matrix is
-questionable. """
-
-
-setup(name = 'lmfit',
- version = versioneer.get_version(),
- cmdclass = versioneer.get_cmdclass(),
- author = 'LMFit Development Team',
- author_email = 'matt.newville at gmail.com',
- url = 'http://lmfit.github.io/lmfit-py/',
- download_url = 'http://lmfit.github.io//lmfit-py/',
- install_requires = ['numpy', 'scipy'],
- license = 'BSD',
- description = "Least-Squares Minimization with Bounds and Constraints",
- long_description = long_desc,
- platforms = ['Windows', 'Linux', 'Mac OS X'],
- classifiers=['Intended Audience :: Science/Research',
- 'Operating System :: OS Independent',
- 'Programming Language :: Python',
- 'Topic :: Scientific/Engineering',
- ],
- # test_suite='nose.collector',
- # test_requires=['Nose'],
- package_dir = {'lmfit': 'lmfit'},
- packages = ['lmfit', 'lmfit.ui', 'lmfit.uncertainties'],
- )
-
+#!/usr/bin/env python
+# from distutils.core import setup
+from setuptools import setup
+
+import versioneer
+versioneer.VCS = 'git'
+versioneer.versionfile_source = 'lmfit/_version.py'
+versioneer.versionfile_build = 'lmfit/_version.py'
+versioneer.tag_prefix = ''
+versioneer.parentdir_prefix = 'lmfit-'
+
+
+long_desc = """A library for least-squares minimization and data fitting in
+Python. Built on top of scipy.optimize, lmfit provides a Parameter object
+which can be set as fixed or free, can have upper and/or lower bounds, or
+can be written in terms of algebraic constraints of other Parameters. The
+user writes a function to be minimized as a function of these Parameters,
+and the scipy.optimize methods are used to find the optimal values for the
+Parameters. The Levenberg-Marquardt (leastsq) is the default minimization
+algorithm, and provides estimated standard errors and correlations between
+varied Parameters. Other minimization methods, including Nelder-Mead's
+downhill simplex, Powell's method, BFGS, Sequential Least Squares, and
+others are also supported. Bounds and contraints can be placed on
+Parameters for all of these methods.
+
+In addition, methods for explicitly calculating confidence intervals are
+provided for exploring minmization problems where the approximation of
+estimating Parameter uncertainties from the covariance matrix is
+questionable. """
+
+
+setup(name = 'lmfit',
+ version = versioneer.get_version(),
+ cmdclass = versioneer.get_cmdclass(),
+ author = 'LMFit Development Team',
+ author_email = 'matt.newville at gmail.com',
+ url = 'http://lmfit.github.io/lmfit-py/',
+ download_url = 'http://lmfit.github.io//lmfit-py/',
+ install_requires = ['numpy', 'scipy'],
+ license = 'BSD',
+ description = "Least-Squares Minimization with Bounds and Constraints",
+ long_description = long_desc,
+ platforms = ['Windows', 'Linux', 'Mac OS X'],
+ classifiers=['Intended Audience :: Science/Research',
+ 'Operating System :: OS Independent',
+ 'Programming Language :: Python',
+ 'Topic :: Scientific/Engineering',
+ ],
+ # test_suite='nose.collector',
+ # test_requires=['Nose'],
+ package_dir = {'lmfit': 'lmfit'},
+ packages = ['lmfit', 'lmfit.ui', 'lmfit.uncertainties'],
+ )
+
diff --git a/tests/NISTModels.py b/tests/NISTModels.py
index 1795653..197856f 100644
--- a/tests/NISTModels.py
+++ b/tests/NISTModels.py
@@ -1,198 +1,198 @@
-import os
-import sys
-from numpy import exp, log, log10, sin, cos, arctan, array
-from lmfit import Parameters
-thisdir, thisfile = os.path.split(__file__)
-NIST_DIR = os.path.join(thisdir, '..', 'NIST_STRD')
-
-def read_params(params):
- if isinstance(params, Parameters):
- return [par.value for par in params.values()]
- else:
- return params
-
-def Bennet5(b, x, y=0):
- b = read_params(b)
- return y - b[0] * (b[1]+x)**(-1/b[2])
-
-def BoxBOD(b, x, y=0):
- b = read_params(b)
- return y - b[0]*(1-exp(-b[1]*x))
-
-def Chwirut(b, x, y=0):
- b = read_params(b)
- return y - exp(-b[0]*x)/(b[1]+b[2]*x)
-
-def DanWood(b, x, y=0):
- b = read_params(b)
- return y - b[0]*x**b[1]
-
-def ENSO(b, x, y=0):
- b = read_params(b)
- pi = 3.141592653589793238462643383279
-
- return y - b[0] + (b[1]*cos( 2*pi*x/12 ) + b[2]*sin( 2*pi*x/12 ) +
- b[4]*cos( 2*pi*x/b[3] ) + b[5]*sin( 2*pi*x/b[3] ) +
- b[7]*cos( 2*pi*x/b[6] ) + b[8]*sin( 2*pi*x/b[6] ) )
-
-def Eckerle4(b, x, y=0):
- b = read_params(b)
- return y - (b[0]/b[1]) * exp(-0.5*((x-b[2])/b[1])**2)
-
-def Gauss(b, x, y=0):
- b = read_params(b)
- return y - b[0]*exp( -b[1]*x ) + (b[2]*exp( -(x-b[3])**2 / b[4]**2 ) +
- b[5]*exp( -(x-b[6])**2 / b[7]**2 ) )
-
-def Hahn1(b, x, y=0):
- b = read_params(b)
- return y - ((b[0]+b[1]*x+b[2]*x**2+b[3]*x**3) /
- (1+b[4]*x+b[5]*x**2+b[6]*x**3) )
-
-def Kirby(b, x, y=0):
- b = read_params(b)
- return y - (b[0] + b[1]*x + b[2]*x**2) / (1 + b[3]*x + b[4]*x**2)
-
-def Lanczos(b, x, y=0):
- b = read_params(b)
- return y - b[0]*exp(-b[1]*x) + b[2]*exp(-b[3]*x) + b[4]*exp(-b[5]*x)
-
-def MGH09(b, x, y=0):
- b = read_params(b)
- return y - b[0]*(x**2+x*b[1]) / (x**2+x*b[2]+b[3])
-
-def MGH10(b, x, y=0):
- b = read_params(b)
- return y - b[0] * exp( b[1]/(x+b[2]) )
-
-def MGH17(b, x, y=0):
- b = read_params(b)
- return y - b[0] + b[1]*exp(-x*b[3]) + b[2]*exp(-x*b[4])
-
-def Misra1a(b, x, y=0):
- b = read_params(b)
- return y - b[0]*(1-exp(-b[1]*x))
-
-def Misra1b(b, x, y=0):
- b = read_params(b)
- return y - b[0] * (1-(1+b[1]*x/2)**(-2))
-
-def Misra1c(b, x, y=0):
- b = read_params(b)
- return y - b[0] * (1-(1+2*b[1]*x)**(-.5))
-
-def Misra1d(b, x, y=0):
- b = read_params(b)
- return y - b[0]*b[1]*x*((1+b[1]*x)**(-1))
-
-def Nelson(b, x, y=None):
- b = read_params(b)
- x1 = x[:,0]
- x2 = x[:,1]
- if y is None:
- return - exp(b[0] - b[1]*x1 * exp(-b[2]*x2))
- return log(y) - (b[0] - b[1]*x1 * exp(-b[2]*x2) )
-
-def Rat42(b, x, y=0):
- b = read_params(b)
- return y - b[0] / (1+exp(b[1]-b[2]*x))
-
-def Rat43(b, x, y=0):
- b = read_params(b)
- return y - b[0] / ((1+exp(b[1]-b[2]*x))**(1/b[3]))
-
-def Roszman1(b, x, y=0):
- b = read_params(b)
- pi = 3.141592653589793238462643383279
- return y - b[0] - b[1]*x - arctan(b[2]/(x-b[3]))/pi
-
-def Thurber(b, x, y=0):
- b = read_params(b)
- return y - ( (b[0] + b[1]*x + b[2]*x**2 + b[3]*x**3) /
- (1 + b[4]*x + b[5]*x**2 + b[6]*x**3) )
-
-# Model name fcn, #fitting params, dim of x
-Models = {'Bennett5': (Bennet5, 3, 1),
- 'BoxBOD': (BoxBOD, 2, 1),
- 'Chwirut1': (Chwirut, 3, 1),
- 'Chwirut2': (Chwirut, 3, 1),
- 'DanWood': (DanWood, 2, 1),
- 'ENSO': (ENSO, 9, 1),
- 'Eckerle4': (Eckerle4, 3, 1),
- 'Gauss1': (Gauss, 8, 1),
- 'Gauss2': (Gauss, 8, 1),
- 'Gauss3': (Gauss, 8, 1),
- 'Hahn1': (Hahn1, 7, 1),
- 'Kirby2': (Kirby, 5, 1),
- 'Lanczos1': (Lanczos, 6, 1),
- 'Lanczos2': (Lanczos, 6, 1),
- 'Lanczos3': (Lanczos, 6, 1),
- 'MGH09': (MGH09, 4, 1),
- 'MGH10': (MGH10, 3, 1),
- 'MGH17': (MGH17, 5, 1),
- 'Misra1a': (Misra1a, 2, 1),
- 'Misra1b' : (Misra1b, 2, 1),
- 'Misra1c' : (Misra1c, 2, 1),
- 'Misra1d' : (Misra1d, 2, 1),
- 'Nelson': (Nelson, 3, 2),
- 'Rat42': (Rat42, 3, 1),
- 'Rat43': (Rat43, 4, 1),
- 'Roszman1': (Roszman1, 4, 1),
- 'Thurber': (Thurber, 7, 1) }
-
-def ReadNistData(dataset):
- """NIST STRD data is in a simple, fixed format with
- line numbers being significant!
- """
- finp = open(os.path.join(NIST_DIR, "%s.dat" % dataset), 'r')
- lines = [l[:-1] for l in finp.readlines()]
- finp.close()
- ModelLines = lines[30:39]
- ParamLines = lines[40:58]
- DataLines = lines[60:]
-
- words = ModelLines[1].strip().split()
- nparams = int(words[0])
-
- start1 = [0]*nparams
- start2 = [0]*nparams
- certval = [0]*nparams
- certerr = [0]*nparams
- for i, text in enumerate(ParamLines[:nparams]):
- [s1, s2, val, err] = [float(x) for x in text.split('=')[1].split()]
- start1[i] = s1
- start2[i] = s2
- certval[i] = val
- certerr[i] = err
-
- #
- for t in ParamLines[nparams:]:
- t = t.strip()
- if ':' not in t:
- continue
- val = float(t.split(':')[1])
- if t.startswith('Residual Sum of Squares'):
- sum_squares = val
- elif t.startswith('Residual Standard Deviation'):
- std_dev = val
- elif t.startswith('Degrees of Freedom'):
- nfree = int(val)
- elif t.startswith('Number of Observations'):
- ndata = int(val)
-
- y, x = [], []
- for d in DataLines:
- vals = [float(i) for i in d.strip().split()]
- y.append(vals[0])
- if len(vals) > 2:
- x.append(vals[1:])
- else:
- x.append(vals[1])
-
- y = array(y)
- x = array(x)
- out = {'y': y, 'x': x, 'nparams': nparams, 'ndata': ndata,
- 'nfree': nfree, 'start1': start1, 'start2': start2,
- 'sum_squares': sum_squares, 'std_dev': std_dev,
- 'cert': certval, 'cert_values': certval, 'cert_stderr': certerr }
- return out
+import os
+import sys
+from numpy import exp, log, log10, sin, cos, arctan, array
+from lmfit import Parameters
+thisdir, thisfile = os.path.split(__file__)
+NIST_DIR = os.path.join(thisdir, '..', 'NIST_STRD')
+
+def read_params(params):
+ if isinstance(params, Parameters):
+ return [par.value for par in params.values()]
+ else:
+ return params
+
+def Bennet5(b, x, y=0):
+ b = read_params(b)
+ return y - b[0] * (b[1]+x)**(-1/b[2])
+
+def BoxBOD(b, x, y=0):
+ b = read_params(b)
+ return y - b[0]*(1-exp(-b[1]*x))
+
+def Chwirut(b, x, y=0):
+ b = read_params(b)
+ return y - exp(-b[0]*x)/(b[1]+b[2]*x)
+
+def DanWood(b, x, y=0):
+ b = read_params(b)
+ return y - b[0]*x**b[1]
+
+def ENSO(b, x, y=0):
+ b = read_params(b)
+ pi = 3.141592653589793238462643383279
+
+ return y - b[0] + (b[1]*cos( 2*pi*x/12 ) + b[2]*sin( 2*pi*x/12 ) +
+ b[4]*cos( 2*pi*x/b[3] ) + b[5]*sin( 2*pi*x/b[3] ) +
+ b[7]*cos( 2*pi*x/b[6] ) + b[8]*sin( 2*pi*x/b[6] ) )
+
+def Eckerle4(b, x, y=0):
+ b = read_params(b)
+ return y - (b[0]/b[1]) * exp(-0.5*((x-b[2])/b[1])**2)
+
+def Gauss(b, x, y=0):
+ b = read_params(b)
+ return y - b[0]*exp( -b[1]*x ) + (b[2]*exp( -(x-b[3])**2 / b[4]**2 ) +
+ b[5]*exp( -(x-b[6])**2 / b[7]**2 ) )
+
+def Hahn1(b, x, y=0):
+ b = read_params(b)
+ return y - ((b[0]+b[1]*x+b[2]*x**2+b[3]*x**3) /
+ (1+b[4]*x+b[5]*x**2+b[6]*x**3) )
+
+def Kirby(b, x, y=0):
+ b = read_params(b)
+ return y - (b[0] + b[1]*x + b[2]*x**2) / (1 + b[3]*x + b[4]*x**2)
+
+def Lanczos(b, x, y=0):
+ b = read_params(b)
+ return y - b[0]*exp(-b[1]*x) + b[2]*exp(-b[3]*x) + b[4]*exp(-b[5]*x)
+
+def MGH09(b, x, y=0):
+ b = read_params(b)
+ return y - b[0]*(x**2+x*b[1]) / (x**2+x*b[2]+b[3])
+
+def MGH10(b, x, y=0):
+ b = read_params(b)
+ return y - b[0] * exp( b[1]/(x+b[2]) )
+
+def MGH17(b, x, y=0):
+ b = read_params(b)
+ return y - b[0] + b[1]*exp(-x*b[3]) + b[2]*exp(-x*b[4])
+
+def Misra1a(b, x, y=0):
+ b = read_params(b)
+ return y - b[0]*(1-exp(-b[1]*x))
+
+def Misra1b(b, x, y=0):
+ b = read_params(b)
+ return y - b[0] * (1-(1+b[1]*x/2)**(-2))
+
+def Misra1c(b, x, y=0):
+ b = read_params(b)
+ return y - b[0] * (1-(1+2*b[1]*x)**(-.5))
+
+def Misra1d(b, x, y=0):
+ b = read_params(b)
+ return y - b[0]*b[1]*x*((1+b[1]*x)**(-1))
+
+def Nelson(b, x, y=None):
+ b = read_params(b)
+ x1 = x[:,0]
+ x2 = x[:,1]
+ if y is None:
+ return - exp(b[0] - b[1]*x1 * exp(-b[2]*x2))
+ return log(y) - (b[0] - b[1]*x1 * exp(-b[2]*x2) )
+
+def Rat42(b, x, y=0):
+ b = read_params(b)
+ return y - b[0] / (1+exp(b[1]-b[2]*x))
+
+def Rat43(b, x, y=0):
+ b = read_params(b)
+ return y - b[0] / ((1+exp(b[1]-b[2]*x))**(1/b[3]))
+
+def Roszman1(b, x, y=0):
+ b = read_params(b)
+ pi = 3.141592653589793238462643383279
+ return y - b[0] - b[1]*x - arctan(b[2]/(x-b[3]))/pi
+
+def Thurber(b, x, y=0):
+ b = read_params(b)
+ return y - ( (b[0] + b[1]*x + b[2]*x**2 + b[3]*x**3) /
+ (1 + b[4]*x + b[5]*x**2 + b[6]*x**3) )
+
+# Model name fcn, #fitting params, dim of x
+Models = {'Bennett5': (Bennet5, 3, 1),
+ 'BoxBOD': (BoxBOD, 2, 1),
+ 'Chwirut1': (Chwirut, 3, 1),
+ 'Chwirut2': (Chwirut, 3, 1),
+ 'DanWood': (DanWood, 2, 1),
+ 'ENSO': (ENSO, 9, 1),
+ 'Eckerle4': (Eckerle4, 3, 1),
+ 'Gauss1': (Gauss, 8, 1),
+ 'Gauss2': (Gauss, 8, 1),
+ 'Gauss3': (Gauss, 8, 1),
+ 'Hahn1': (Hahn1, 7, 1),
+ 'Kirby2': (Kirby, 5, 1),
+ 'Lanczos1': (Lanczos, 6, 1),
+ 'Lanczos2': (Lanczos, 6, 1),
+ 'Lanczos3': (Lanczos, 6, 1),
+ 'MGH09': (MGH09, 4, 1),
+ 'MGH10': (MGH10, 3, 1),
+ 'MGH17': (MGH17, 5, 1),
+ 'Misra1a': (Misra1a, 2, 1),
+ 'Misra1b' : (Misra1b, 2, 1),
+ 'Misra1c' : (Misra1c, 2, 1),
+ 'Misra1d' : (Misra1d, 2, 1),
+ 'Nelson': (Nelson, 3, 2),
+ 'Rat42': (Rat42, 3, 1),
+ 'Rat43': (Rat43, 4, 1),
+ 'Roszman1': (Roszman1, 4, 1),
+ 'Thurber': (Thurber, 7, 1) }
+
+def ReadNistData(dataset):
+ """NIST STRD data is in a simple, fixed format with
+ line numbers being significant!
+ """
+ finp = open(os.path.join(NIST_DIR, "%s.dat" % dataset), 'r')
+ lines = [l[:-1] for l in finp.readlines()]
+ finp.close()
+ ModelLines = lines[30:39]
+ ParamLines = lines[40:58]
+ DataLines = lines[60:]
+
+ words = ModelLines[1].strip().split()
+ nparams = int(words[0])
+
+ start1 = [0]*nparams
+ start2 = [0]*nparams
+ certval = [0]*nparams
+ certerr = [0]*nparams
+ for i, text in enumerate(ParamLines[:nparams]):
+ [s1, s2, val, err] = [float(x) for x in text.split('=')[1].split()]
+ start1[i] = s1
+ start2[i] = s2
+ certval[i] = val
+ certerr[i] = err
+
+ #
+ for t in ParamLines[nparams:]:
+ t = t.strip()
+ if ':' not in t:
+ continue
+ val = float(t.split(':')[1])
+ if t.startswith('Residual Sum of Squares'):
+ sum_squares = val
+ elif t.startswith('Residual Standard Deviation'):
+ std_dev = val
+ elif t.startswith('Degrees of Freedom'):
+ nfree = int(val)
+ elif t.startswith('Number of Observations'):
+ ndata = int(val)
+
+ y, x = [], []
+ for d in DataLines:
+ vals = [float(i) for i in d.strip().split()]
+ y.append(vals[0])
+ if len(vals) > 2:
+ x.append(vals[1:])
+ else:
+ x.append(vals[1])
+
+ y = array(y)
+ x = array(x)
+ out = {'y': y, 'x': x, 'nparams': nparams, 'ndata': ndata,
+ 'nfree': nfree, 'start1': start1, 'start2': start2,
+ 'sum_squares': sum_squares, 'std_dev': std_dev,
+ 'cert': certval, 'cert_values': certval, 'cert_stderr': certerr }
+ return out
diff --git a/tests/_test_ci.py b/tests/_test_ci.py
index bbb767e..86afcaf 100644
--- a/tests/_test_ci.py
+++ b/tests/_test_ci.py
@@ -1,58 +1,58 @@
-from __future__ import print_function
-from lmfit import minimize, Parameters, conf_interval, report_ci, report_errors
-import numpy as np
-pi = np.pi
-import nose
-
-def test_ci():
- np.random.seed(1)
- p_true = Parameters()
- p_true.add('amp', value=14.0)
- p_true.add('period', value=5.33)
- p_true.add('shift', value=0.123)
- p_true.add('decay', value=0.010)
-
- def residual(pars, x, data=None):
- amp = pars['amp'].value
- per = pars['period'].value
- shift = pars['shift'].value
- decay = pars['decay'].value
-
- if abs(shift) > pi / 2:
- shift = shift - np.sign(shift) * pi
- model = amp * np.sin(shift + x / per) * np.exp(-x * x * decay * decay)
- if data is None:
- return model
- return model - data
-
-
- n = 2500
- xmin = 0.
- xmax = 250.0
- noise = np.random.normal(scale=0.7215, size=n)
- x = np.linspace(xmin, xmax, n)
- data = residual(p_true, x) + noise
-
- fit_params = Parameters()
- fit_params.add('amp', value=13.0)
- fit_params.add('period', value=4)
- fit_params.add('shift', value=0.1)
- fit_params.add('decay', value=0.02)
-
- out = minimize(residual, fit_params, args=(x,), kws={'data': data})
-
- fit = residual(fit_params, x)
-
- print( ' N fev = ', out.nfev)
- print( out.chisqr, out.redchi, out.nfree)
-
- report_errors(fit_params)
- ci, tr = conf_interval(out, sigmas=[0.674], trace=True)
- report_ci(ci)
- for p in out.params:
- diff1 = ci[p][1][1] - ci[p][0][1]
- diff2 = ci[p][2][1] - ci[p][1][1]
- stderr = out.params[p].stderr
- assert(abs(diff1 - stderr) / stderr < 0.05)
- assert(abs(diff2 - stderr) / stderr < 0.05)
-
+from __future__ import print_function
+from lmfit import minimize, Parameters, conf_interval, report_ci, report_errors
+import numpy as np
+pi = np.pi
+import nose
+
+def test_ci():
+ np.random.seed(1)
+ p_true = Parameters()
+ p_true.add('amp', value=14.0)
+ p_true.add('period', value=5.33)
+ p_true.add('shift', value=0.123)
+ p_true.add('decay', value=0.010)
+
+ def residual(pars, x, data=None):
+ amp = pars['amp'].value
+ per = pars['period'].value
+ shift = pars['shift'].value
+ decay = pars['decay'].value
+
+ if abs(shift) > pi / 2:
+ shift = shift - np.sign(shift) * pi
+ model = amp * np.sin(shift + x / per) * np.exp(-x * x * decay * decay)
+ if data is None:
+ return model
+ return model - data
+
+
+ n = 2500
+ xmin = 0.
+ xmax = 250.0
+ noise = np.random.normal(scale=0.7215, size=n)
+ x = np.linspace(xmin, xmax, n)
+ data = residual(p_true, x) + noise
+
+ fit_params = Parameters()
+ fit_params.add('amp', value=13.0)
+ fit_params.add('period', value=4)
+ fit_params.add('shift', value=0.1)
+ fit_params.add('decay', value=0.02)
+
+ out = minimize(residual, fit_params, args=(x,), kws={'data': data})
+
+ fit = residual(fit_params, x)
+
+ print( ' N fev = ', out.nfev)
+ print( out.chisqr, out.redchi, out.nfree)
+
+ report_errors(fit_params)
+ ci, tr = conf_interval(out, sigmas=[0.674], trace=True)
+ report_ci(ci)
+ for p in out.params:
+ diff1 = ci[p][1][1] - ci[p][0][1]
+ diff2 = ci[p][2][1] - ci[p][1][1]
+ stderr = out.params[p].stderr
+ assert(abs(diff1 - stderr) / stderr < 0.05)
+ assert(abs(diff2 - stderr) / stderr < 0.05)
+
diff --git a/tests/_test_make_paras_and_func.py b/tests/_test_make_paras_and_func.py
index ee0a251..7a7b27f 100644
--- a/tests/_test_make_paras_and_func.py
+++ b/tests/_test_make_paras_and_func.py
@@ -1,31 +1,31 @@
-# -*- coding: utf-8 -*-
-
-import lmfit
-
-
-def test_wrap_function():
- get_names = lambda p: [p_key for p_key in p ]
-
- def func(A, b, c, d=5, e=10):
- return A + b + c + d
-
- x0 = [1, 2, 3]
- para, f = lmfit.make_paras_and_func(func, x0)
- assert(get_names(para) == ['A', 'b', 'c'])
- y1 = f(para)
- y2 = func(*x0)
- assert(y1==y2)
-
- x0 = [1, 2, 3, 4]
- para, f = lmfit.make_paras_and_func(func, x0)
- assert(get_names(para) == ['A', 'b', 'c', 'd'])
- y1 = f(para)
- y2 = func(*x0)
- assert(y1==y2)
-
- x0 = [1, 2, 3]
- para, f = lmfit.make_paras_and_func(func, x0, {'e': 3})
- assert(get_names(para) == ['A', 'b', 'c', 'e'])
- y1 = f(para)
- y2 = func(*x0)
- assert(y1==y2)
+# -*- coding: utf-8 -*-
+
+import lmfit
+
+
+def test_wrap_function():
+ get_names = lambda p: [p_key for p_key in p ]
+
+ def func(A, b, c, d=5, e=10):
+ return A + b + c + d
+
+ x0 = [1, 2, 3]
+ para, f = lmfit.make_paras_and_func(func, x0)
+ assert(get_names(para) == ['A', 'b', 'c'])
+ y1 = f(para)
+ y2 = func(*x0)
+ assert(y1==y2)
+
+ x0 = [1, 2, 3, 4]
+ para, f = lmfit.make_paras_and_func(func, x0)
+ assert(get_names(para) == ['A', 'b', 'c', 'd'])
+ y1 = f(para)
+ y2 = func(*x0)
+ assert(y1==y2)
+
+ x0 = [1, 2, 3]
+ para, f = lmfit.make_paras_and_func(func, x0, {'e': 3})
+ assert(get_names(para) == ['A', 'b', 'c', 'e'])
+ y1 = f(para)
+ y2 = func(*x0)
+ assert(y1==y2)
diff --git a/tests/lmfit_testutils.py b/tests/lmfit_testutils.py
index f399f2c..79e89d4 100644
--- a/tests/lmfit_testutils.py
+++ b/tests/lmfit_testutils.py
@@ -1,18 +1,18 @@
-from lmfit import Parameter
-from numpy.testing import assert_allclose
-
-def assert_paramval(param, val, tol=1.e-3):
- """assert that a named parameter's value is close to expected value"""
-
- assert(isinstance(param, Parameter))
- pval = param.value
-
- assert_allclose([pval], [val], rtol=tol, atol=tol,
- err_msg='',verbose=True)
-
-def assert_paramattr(param, attr, val):
- """assert that a named parameter's value is a value"""
- assert(isinstance(param, Parameter))
- assert(hasattr(param, attr))
- assert(getattr(param, attr) == val)
-
+from lmfit import Parameter
+from numpy.testing import assert_allclose
+
+def assert_paramval(param, val, tol=1.e-3):
+ """assert that a named parameter's value is close to expected value"""
+
+ assert(isinstance(param, Parameter))
+ pval = param.value
+
+ assert_allclose([pval], [val], rtol=tol, atol=tol,
+ err_msg='',verbose=True)
+
+def assert_paramattr(param, attr, val):
+ """assert that a named parameter's value is a value"""
+ assert(isinstance(param, Parameter))
+ assert(hasattr(param, attr))
+ assert(getattr(param, attr) == val)
+
diff --git a/tests/test_1variable.py b/tests/test_1variable.py
index a832f79..3e3d530 100644
--- a/tests/test_1variable.py
+++ b/tests/test_1variable.py
@@ -1,57 +1,57 @@
-# test of fitting one variable
-# From Nick Schurch
-
-import lmfit, numpy
-from numpy.testing import assert_allclose
-
-def linear_chisq(params, x, data, errs=None):
-
- ''' Calcs chi-squared residuals linear model (weighted by errors if given)
- '''
-
- if type(params) is not lmfit.parameter.Parameters:
- msg = "Params argument is not a lmfit parameter set"
- raise TypeError(msg)
-
- if "m" not in params.keys():
- msg = "No slope parameter (m) defined in the model"
- raise KeyError(msg)
-
- if "c" not in params.keys():
- msg = "No intercept parameter (c) defined in the model"
- raise KeyError(msg)
-
- m = params["m"].value
- c = params["c"].value
-
- model = m*x+c
-
- residuals = (data-model)
- if errs is not None:
- residuals = residuals/errs
-
- return(residuals)
-
-def test_1var():
- rands = [-0.21698284, 0.41900591, 0.02349374, -0.218552, -0.3513699,
- 0.33418304, 0.04226855, 0.213303, 0.45948731, 0.33587736]
-
- x = numpy.arange(10)+1
- y = numpy.arange(10)+1+rands
- y_errs = numpy.sqrt(y)/2
-
- params = lmfit.Parameters()
- params.add(name="m", value=1.0, vary=True)
- params.add(name="c", value=0.0, vary=False)
-
- out = lmfit.minimize(linear_chisq, params, args=(x, y))
-
- lmfit.report_fit(out)
- assert_allclose(params['m'].value, 1.025, rtol=0.02, atol=0.02)
- assert(len(params)==2)
- assert(out.nvarys == 1)
- assert(out.chisqr > 0.01)
- assert(out.chisqr < 5.00)
-
-if __name__ == '__main__':
- test_1var()
+# test of fitting one variable
+# From Nick Schurch
+
+import lmfit, numpy
+from numpy.testing import assert_allclose
+
+def linear_chisq(params, x, data, errs=None):
+
+ ''' Calcs chi-squared residuals linear model (weighted by errors if given)
+ '''
+
+ if type(params) is not lmfit.parameter.Parameters:
+ msg = "Params argument is not a lmfit parameter set"
+ raise TypeError(msg)
+
+ if "m" not in params.keys():
+ msg = "No slope parameter (m) defined in the model"
+ raise KeyError(msg)
+
+ if "c" not in params.keys():
+ msg = "No intercept parameter (c) defined in the model"
+ raise KeyError(msg)
+
+ m = params["m"].value
+ c = params["c"].value
+
+ model = m*x+c
+
+ residuals = (data-model)
+ if errs is not None:
+ residuals = residuals/errs
+
+ return(residuals)
+
+def test_1var():
+ rands = [-0.21698284, 0.41900591, 0.02349374, -0.218552, -0.3513699,
+ 0.33418304, 0.04226855, 0.213303, 0.45948731, 0.33587736]
+
+ x = numpy.arange(10)+1
+ y = numpy.arange(10)+1+rands
+ y_errs = numpy.sqrt(y)/2
+
+ params = lmfit.Parameters()
+ params.add(name="m", value=1.0, vary=True)
+ params.add(name="c", value=0.0, vary=False)
+
+ out = lmfit.minimize(linear_chisq, params, args=(x, y))
+
+ lmfit.report_fit(out)
+ assert_allclose(params['m'].value, 1.025, rtol=0.02, atol=0.02)
+ assert(len(params)==2)
+ assert(out.nvarys == 1)
+ assert(out.chisqr > 0.01)
+ assert(out.chisqr < 5.00)
+
+if __name__ == '__main__':
+ test_1var()
diff --git a/tests/test_NIST_Strd.py b/tests/test_NIST_Strd.py
index 0ce77f6..aec9a8f 100644
--- a/tests/test_NIST_Strd.py
+++ b/tests/test_NIST_Strd.py
@@ -1,267 +1,267 @@
-from __future__ import print_function
-import sys
-import math
-from optparse import OptionParser
-
-from lmfit import Parameters, minimize
-
-from NISTModels import Models, ReadNistData
-
-HASPYLAB = False
-for arg in sys.argv:
- if 'nose' in arg:
- HASPYLAB = False
-
-if HASPYLAB:
- try:
- import matplotlib
- import pylab
- HASPYLAB = True
- except ImportError:
- HASPYLAB = False
-
-def ndig(a, b):
- "precision for NIST values"
- return round(-math.log10((abs(abs(a)-abs(b)) +1.e-15)/ abs(b)))
-
-ABAR = ' |----------------+----------------+------------------+-------------------|'
-def Compare_NIST_Results(DataSet, myfit, params, NISTdata):
- buff = [' ======================================',
- ' %s: ' % DataSet,
- ' | Parameter Name | Value Found | Certified Value | # Matching Digits |']
- buff.append(ABAR)
-
- val_dig_min = 200
- err_dig_min = 200
- fmt = ' | %s | % -.7e | % -.7e | %2i |'
- for i in range(NISTdata['nparams']):
- parname = 'b%i' % (i+1)
- par = params[parname]
- thisval = par.value
- certval = NISTdata['cert_values'][i]
- vdig = ndig(thisval, certval)
- pname = (parname + ' value ' + ' '*14)[:14]
- buff.append(fmt % (pname, thisval, certval, vdig))
- val_dig_min = min(val_dig_min, vdig)
-
- thiserr = par.stderr
- certerr = NISTdata['cert_stderr'][i]
- if thiserr is not None and myfit.errorbars:
- edig = ndig(thiserr, certerr)
- ename = (parname + ' stderr' + ' '*14)[:14]
- buff.append(fmt % (ename, thiserr, certerr, edig))
- err_dig_min = min(err_dig_min, edig)
-
- buff.append(ABAR)
- sumsq = NISTdata['sum_squares']
- try:
- chi2 = myfit.chisqr
- buff.append(' | Sum of Squares | %.7e | %.7e | %2i |'
- % (chi2, sumsq, ndig(chi2, sumsq)))
- except:
- pass
- buff.append(ABAR)
- if not myfit.errorbars:
- buff.append(' | * * * * COULD NOT ESTIMATE UNCERTAINTIES * * * * |')
- err_dig_min = 0
- if err_dig_min < 199:
- buff.append(' Worst agreement: %i digits for value, %i digits for error '
- % (val_dig_min, err_dig_min))
- else:
- buff.append(' Worst agreement: %i digits' % (val_dig_min))
- return val_dig_min, '\n'.join(buff)
-
-def NIST_Dataset(DataSet, method='leastsq', start='start2',
- plot=True, verbose=False):
-
- NISTdata = ReadNistData(DataSet)
- resid, npar, dimx = Models[DataSet]
- y = NISTdata['y']
- x = NISTdata['x']
-
- params = Parameters()
- for i in range(npar):
- pname = 'b%i' % (i+1)
- cval = NISTdata['cert_values'][i]
- cerr = NISTdata['cert_stderr'][i]
- pval1 = NISTdata[start][i]
- params.add(pname, value=pval1)
-
- myfit = minimize(resid, params, method=method, args=(x,), kws={'y':y})
- digs, buff = Compare_NIST_Results(DataSet, myfit, myfit.params, NISTdata)
- if verbose:
- print(buff)
- if plot and HASPYLAB:
- fit = -resid(myfit.params, x, )
- pylab.plot(x, y, 'ro')
- pylab.plot(x, fit, 'k+-')
- pylab.show()
-
- return digs > 1
-
-def build_usage():
- modelnames = []
- ms = ''
- for d in sorted(Models.keys()):
- ms = ms + ' %s ' % d
- if len(ms) > 55:
- modelnames.append(ms)
- ms = ' '
- modelnames.append(ms)
- modelnames = '\n'.join(modelnames)
-
- usage = """
- === Test Fit to NIST StRD Models ===
-
-usage:
-------
- python fit_NIST.py [options] Model Start
-
-where Start is one of 'start1','start2' or 'cert', for different
-starting values, and Model is one of
-
- %s
-
-if Model = 'all', all models and starting values will be run.
-
-options:
---------
- -m name of fitting method. One of:
- leastsq, nelder, powell, lbfgsb, bfgs,
- tnc, cobyla, slsqp, cg, newto-cg
- leastsq (Levenberg-Marquardt) is the default
-""" % modelnames
- return usage
-
-############################
-def run_interactive():
- usage = build_usage()
- parser = OptionParser(usage=usage, prog="fit-NIST.py")
-
- parser.add_option("-m", "--method", dest="method",
- metavar='METH',
- default='leastsq',
- help="set method name, default = 'leastsq'")
-
- (opts, args) = parser.parse_args()
- dset = ''
- start = 'start2'
- if len(args) > 0:
- dset = args[0]
- if len(args) > 1:
- start = args[1]
-
- if dset.lower() == 'all':
- tpass = 0
- tfail = 0
- failures = []
- dsets = sorted(Models.keys())
- for dset in dsets:
- for start in ('start1', 'start2', 'cert'):
- if NIST_Dataset(dset, method=opts.method, start=start,
- plot=False, verbose=True):
- tpass += 1
- else:
- tfail += 1
- failures.append(" %s (starting at '%s')" % (dset, start))
- print('--------------------------------------')
- print(' Fit Method: %s ' % opts.method)
- print(' Final Results: %i pass, %i fail.' % (tpass, tfail))
- print(' Tests Failed for:\n %s' % '\n '.join(failures))
- print('--------------------------------------')
- elif dset not in Models:
- print(usage)
- else:
- return NIST_Dataset(dset, method=opts.method,
- start=start, plot=True, verbose=True)
-
-def RunNIST_Model(model):
- out1 = NIST_Dataset(model, start='start1', plot=False, verbose=False)
- out2 = NIST_Dataset(model, start='start2', plot=False, verbose=False)
- print("NIST Test" , model, out1, out2)
- assert(out1 or out2)
- return out1 or out2
-
-def test_Bennett5():
- return RunNIST_Model('Bennett5')
-
-def test_BoxBOD():
- return RunNIST_Model('BoxBOD')
-
-def test_Chwirut1():
- return RunNIST_Model('Chwirut1')
-
-def test_Chwirut2():
- return RunNIST_Model('Chwirut2')
-
-def test_DanWood():
- return RunNIST_Model('DanWood')
-
-def test_ENSO():
- return RunNIST_Model('ENSO')
-
-def test_Eckerle4():
- return RunNIST_Model('Eckerle4')
-
-def test_Gauss1():
- return RunNIST_Model('Gauss1')
-
-def test_Gauss2():
- return RunNIST_Model('Gauss2')
-
-def test_Gauss3():
- return RunNIST_Model('Gauss3')
-
-def test_Hahn1():
- return RunNIST_Model('Hahn1')
-
-def test_Kirby2():
- return RunNIST_Model('Kirby2')
-
-def test_Lanczos1():
- return RunNIST_Model('Lanczos1')
-
-def test_Lanczos2():
- return RunNIST_Model('Lanczos2')
-
-def test_Lanczos3():
- return RunNIST_Model('Lanczos3')
-
-def test_MGH09():
- return RunNIST_Model('MGH09')
-
-def test_MGH10():
- return RunNIST_Model('MGH10')
-
-def test_MGH17():
- return RunNIST_Model('MGH17')
-
-def test_Misra1a():
- return RunNIST_Model('Misra1a')
-
-def test_Misra1b():
- return RunNIST_Model('Misra1b')
-
-def test_Misra1c():
- return RunNIST_Model('Misra1c')
-
-def test_Misra1d():
- return RunNIST_Model('Misra1d')
-
-def test_Nelson():
- return RunNIST_Model('Nelson')
-
-def test_Rat42():
- return RunNIST_Model('Rat42')
-
-def test_Rat43():
- return RunNIST_Model('Rat43')
-
-def test_Roszman1():
- return RunNIST_Model('Roszman1')
-
-def test_Thurber():
- return RunNIST_Model('Thurber')
-
-if __name__ == '__main__':
- run_interactive()
+from __future__ import print_function
+import sys
+import math
+from optparse import OptionParser
+
+from lmfit import Parameters, minimize
+
+from NISTModels import Models, ReadNistData
+
+HASPYLAB = False
+for arg in sys.argv:
+ if 'nose' in arg:
+ HASPYLAB = False
+
+if HASPYLAB:
+ try:
+ import matplotlib
+ import pylab
+ HASPYLAB = True
+ except ImportError:
+ HASPYLAB = False
+
+def ndig(a, b):
+ "precision for NIST values"
+ return round(-math.log10((abs(abs(a)-abs(b)) +1.e-15)/ abs(b)))
+
+ABAR = ' |----------------+----------------+------------------+-------------------|'
+def Compare_NIST_Results(DataSet, myfit, params, NISTdata):
+ buff = [' ======================================',
+ ' %s: ' % DataSet,
+ ' | Parameter Name | Value Found | Certified Value | # Matching Digits |']
+ buff.append(ABAR)
+
+ val_dig_min = 200
+ err_dig_min = 200
+ fmt = ' | %s | % -.7e | % -.7e | %2i |'
+ for i in range(NISTdata['nparams']):
+ parname = 'b%i' % (i+1)
+ par = params[parname]
+ thisval = par.value
+ certval = NISTdata['cert_values'][i]
+ vdig = ndig(thisval, certval)
+ pname = (parname + ' value ' + ' '*14)[:14]
+ buff.append(fmt % (pname, thisval, certval, vdig))
+ val_dig_min = min(val_dig_min, vdig)
+
+ thiserr = par.stderr
+ certerr = NISTdata['cert_stderr'][i]
+ if thiserr is not None and myfit.errorbars:
+ edig = ndig(thiserr, certerr)
+ ename = (parname + ' stderr' + ' '*14)[:14]
+ buff.append(fmt % (ename, thiserr, certerr, edig))
+ err_dig_min = min(err_dig_min, edig)
+
+ buff.append(ABAR)
+ sumsq = NISTdata['sum_squares']
+ try:
+ chi2 = myfit.chisqr
+ buff.append(' | Sum of Squares | %.7e | %.7e | %2i |'
+ % (chi2, sumsq, ndig(chi2, sumsq)))
+ except:
+ pass
+ buff.append(ABAR)
+ if not myfit.errorbars:
+ buff.append(' | * * * * COULD NOT ESTIMATE UNCERTAINTIES * * * * |')
+ err_dig_min = 0
+ if err_dig_min < 199:
+ buff.append(' Worst agreement: %i digits for value, %i digits for error '
+ % (val_dig_min, err_dig_min))
+ else:
+ buff.append(' Worst agreement: %i digits' % (val_dig_min))
+ return val_dig_min, '\n'.join(buff)
+
+def NIST_Dataset(DataSet, method='leastsq', start='start2',
+ plot=True, verbose=False):
+
+ NISTdata = ReadNistData(DataSet)
+ resid, npar, dimx = Models[DataSet]
+ y = NISTdata['y']
+ x = NISTdata['x']
+
+ params = Parameters()
+ for i in range(npar):
+ pname = 'b%i' % (i+1)
+ cval = NISTdata['cert_values'][i]
+ cerr = NISTdata['cert_stderr'][i]
+ pval1 = NISTdata[start][i]
+ params.add(pname, value=pval1)
+
+ myfit = minimize(resid, params, method=method, args=(x,), kws={'y':y})
+ digs, buff = Compare_NIST_Results(DataSet, myfit, myfit.params, NISTdata)
+ if verbose:
+ print(buff)
+ if plot and HASPYLAB:
+ fit = -resid(myfit.params, x, )
+ pylab.plot(x, y, 'ro')
+ pylab.plot(x, fit, 'k+-')
+ pylab.show()
+
+ return digs > 1
+
+def build_usage():
+ modelnames = []
+ ms = ''
+ for d in sorted(Models.keys()):
+ ms = ms + ' %s ' % d
+ if len(ms) > 55:
+ modelnames.append(ms)
+ ms = ' '
+ modelnames.append(ms)
+ modelnames = '\n'.join(modelnames)
+
+ usage = """
+ === Test Fit to NIST StRD Models ===
+
+usage:
+------
+ python fit_NIST.py [options] Model Start
+
+where Start is one of 'start1','start2' or 'cert', for different
+starting values, and Model is one of
+
+ %s
+
+if Model = 'all', all models and starting values will be run.
+
+options:
+--------
+ -m name of fitting method. One of:
+ leastsq, nelder, powell, lbfgsb, bfgs,
+ tnc, cobyla, slsqp, cg, newto-cg
+ leastsq (Levenberg-Marquardt) is the default
+""" % modelnames
+ return usage
+
+############################
+def run_interactive():
+ usage = build_usage()
+ parser = OptionParser(usage=usage, prog="fit-NIST.py")
+
+ parser.add_option("-m", "--method", dest="method",
+ metavar='METH',
+ default='leastsq',
+ help="set method name, default = 'leastsq'")
+
+ (opts, args) = parser.parse_args()
+ dset = ''
+ start = 'start2'
+ if len(args) > 0:
+ dset = args[0]
+ if len(args) > 1:
+ start = args[1]
+
+ if dset.lower() == 'all':
+ tpass = 0
+ tfail = 0
+ failures = []
+ dsets = sorted(Models.keys())
+ for dset in dsets:
+ for start in ('start1', 'start2', 'cert'):
+ if NIST_Dataset(dset, method=opts.method, start=start,
+ plot=False, verbose=True):
+ tpass += 1
+ else:
+ tfail += 1
+ failures.append(" %s (starting at '%s')" % (dset, start))
+ print('--------------------------------------')
+ print(' Fit Method: %s ' % opts.method)
+ print(' Final Results: %i pass, %i fail.' % (tpass, tfail))
+ print(' Tests Failed for:\n %s' % '\n '.join(failures))
+ print('--------------------------------------')
+ elif dset not in Models:
+ print(usage)
+ else:
+ return NIST_Dataset(dset, method=opts.method,
+ start=start, plot=True, verbose=True)
+
+def RunNIST_Model(model):
+ out1 = NIST_Dataset(model, start='start1', plot=False, verbose=False)
+ out2 = NIST_Dataset(model, start='start2', plot=False, verbose=False)
+ print("NIST Test" , model, out1, out2)
+ assert(out1 or out2)
+ return out1 or out2
+
+def test_Bennett5():
+ return RunNIST_Model('Bennett5')
+
+def test_BoxBOD():
+ return RunNIST_Model('BoxBOD')
+
+def test_Chwirut1():
+ return RunNIST_Model('Chwirut1')
+
+def test_Chwirut2():
+ return RunNIST_Model('Chwirut2')
+
+def test_DanWood():
+ return RunNIST_Model('DanWood')
+
+def test_ENSO():
+ return RunNIST_Model('ENSO')
+
+def test_Eckerle4():
+ return RunNIST_Model('Eckerle4')
+
+def test_Gauss1():
+ return RunNIST_Model('Gauss1')
+
+def test_Gauss2():
+ return RunNIST_Model('Gauss2')
+
+def test_Gauss3():
+ return RunNIST_Model('Gauss3')
+
+def test_Hahn1():
+ return RunNIST_Model('Hahn1')
+
+def test_Kirby2():
+ return RunNIST_Model('Kirby2')
+
+def test_Lanczos1():
+ return RunNIST_Model('Lanczos1')
+
+def test_Lanczos2():
+ return RunNIST_Model('Lanczos2')
+
+def test_Lanczos3():
+ return RunNIST_Model('Lanczos3')
+
+def test_MGH09():
+ return RunNIST_Model('MGH09')
+
+def test_MGH10():
+ return RunNIST_Model('MGH10')
+
+def test_MGH17():
+ return RunNIST_Model('MGH17')
+
+def test_Misra1a():
+ return RunNIST_Model('Misra1a')
+
+def test_Misra1b():
+ return RunNIST_Model('Misra1b')
+
+def test_Misra1c():
+ return RunNIST_Model('Misra1c')
+
+def test_Misra1d():
+ return RunNIST_Model('Misra1d')
+
+def test_Nelson():
+ return RunNIST_Model('Nelson')
+
+def test_Rat42():
+ return RunNIST_Model('Rat42')
+
+def test_Rat43():
+ return RunNIST_Model('Rat43')
+
+def test_Roszman1():
+ return RunNIST_Model('Roszman1')
+
+def test_Thurber():
+ return RunNIST_Model('Thurber')
+
+if __name__ == '__main__':
+ run_interactive()
diff --git a/tests/test_algebraic_constraint.py b/tests/test_algebraic_constraint.py
index a256169..1764b7f 100644
--- a/tests/test_algebraic_constraint.py
+++ b/tests/test_algebraic_constraint.py
@@ -1,135 +1,159 @@
-from numpy import linspace, zeros, sin, exp, random, sqrt, pi, sign
-from lmfit import Parameters, Parameter, Minimizer
-from lmfit.lineshapes import gaussian, lorentzian, pvoigt
-from lmfit.printfuncs import report_fit
-
-def test_constraints1():
- def residual(pars, x, sigma=None, data=None):
- yg = gaussian(x, pars['amp_g'].value,
- pars['cen_g'].value, pars['wid_g'].value)
- yl = lorentzian(x, pars['amp_l'].value,
- pars['cen_l'].value, pars['wid_l'].value)
-
- slope = pars['line_slope'].value
- offset = pars['line_off'].value
- model = yg + yl + offset + x * slope
- if data is None:
- return model
- if sigma is None:
- return (model - data)
- return (model - data)/sigma
-
-
- n = 601
- xmin = 0.
- xmax = 20.0
- x = linspace(xmin, xmax, n)
-
- data = (gaussian(x, 21, 8.1, 1.2) +
- lorentzian(x, 10, 9.6, 2.4) +
- random.normal(scale=0.23, size=n) +
- x*0.5)
-
-
- pfit = Parameters()
- pfit.add(name='amp_g', value=10)
- pfit.add(name='cen_g', value=9)
- pfit.add(name='wid_g', value=1)
-
- pfit.add(name='amp_tot', value=20)
- pfit.add(name='amp_l', expr='amp_tot - amp_g')
- pfit.add(name='cen_l', expr='1.5+cen_g')
- pfit.add(name='wid_l', expr='2*wid_g')
-
- pfit.add(name='line_slope', value=0.0)
- pfit.add(name='line_off', value=0.0)
-
- sigma = 0.021 # estimate of data error (for all data points)
-
- myfit = Minimizer(residual, pfit,
- fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
- scale_covar=True)
-
- myfit.prepare_fit()
- init = residual(myfit.params, x)
-
- result = myfit.leastsq()
-
- print(' Nfev = ', result.nfev)
- print( result.chisqr, result.redchi, result.nfree)
-
- report_fit(result.params)
- pfit= result.params
- fit = residual(result.params, x)
- assert(pfit['cen_l'].value == 1.5 + pfit['cen_g'].value)
- assert(pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value)
- assert(pfit['wid_l'].value == 2 * pfit['wid_g'].value)
-
-
-def test_constraints2():
- """add a user-defined function to symbol table"""
- def residual(pars, x, sigma=None, data=None):
- yg = gaussian(x, pars['amp_g'].value,
- pars['cen_g'].value, pars['wid_g'].value)
- yl = lorentzian(x, pars['amp_l'].value,
- pars['cen_l'].value, pars['wid_l'].value)
-
- slope = pars['line_slope'].value
- offset = pars['line_off'].value
- model = yg + yl + offset + x * slope
- if data is None:
- return model
- if sigma is None:
- return (model - data)
- return (model - data)/sigma
-
-
- n = 601
- xmin = 0.
- xmax = 20.0
- x = linspace(xmin, xmax, n)
-
- data = (gaussian(x, 21, 8.1, 1.2) +
- lorentzian(x, 10, 9.6, 2.4) +
- random.normal(scale=0.23, size=n) +
- x*0.5)
-
- pfit = Parameters()
- pfit.add(name='amp_g', value=10)
- pfit.add(name='cen_g', value=9)
- pfit.add(name='wid_g', value=1)
-
- pfit.add(name='amp_tot', value=20)
- pfit.add(name='amp_l', expr='amp_tot - amp_g')
- pfit.add(name='cen_l', expr='1.5+cen_g')
- pfit.add(name='line_slope', value=0.0)
- pfit.add(name='line_off', value=0.0)
-
- sigma = 0.021 # estimate of data error (for all data points)
-
- myfit = Minimizer(residual, pfit,
- fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
- scale_covar=True)
-
- def width_func(wpar):
- """ """
- return 2*wpar
-
- myfit.params._asteval.symtable['wfun'] = width_func
- myfit.params.add(name='wid_l', expr='wfun(wid_g)')
-
- result = myfit.leastsq()
-
- print(' Nfev = ', result.nfev)
- print( result.chisqr, result.redchi, result.nfree)
-
- report_fit(result.params)
- pfit= result.params
- fit = residual(result.params, x)
- assert(pfit['cen_l'].value == 1.5 + pfit['cen_g'].value)
- assert(pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value)
- assert(pfit['wid_l'].value == 2 * pfit['wid_g'].value)
-
-if __name__ == '__main__':
- test_constraints1()
- test_constraints2()
+from numpy import linspace, zeros, sin, exp, random, sqrt, pi, sign
+from lmfit import Parameters, Parameter, Minimizer, Model
+from lmfit.lineshapes import gaussian, lorentzian, pvoigt
+from lmfit.printfuncs import report_fit
+
+def test_constraints1():
+ def residual(pars, x, sigma=None, data=None):
+ yg = gaussian(x, pars['amp_g'].value,
+ pars['cen_g'].value, pars['wid_g'].value)
+ yl = lorentzian(x, pars['amp_l'].value,
+ pars['cen_l'].value, pars['wid_l'].value)
+
+ slope = pars['line_slope'].value
+ offset = pars['line_off'].value
+ model = yg + yl + offset + x * slope
+ if data is None:
+ return model
+ if sigma is None:
+ return (model - data)
+ return (model - data)/sigma
+
+
+ n = 601
+ xmin = 0.
+ xmax = 20.0
+ x = linspace(xmin, xmax, n)
+
+ data = (gaussian(x, 21, 8.1, 1.2) +
+ lorentzian(x, 10, 9.6, 2.4) +
+ random.normal(scale=0.23, size=n) +
+ x*0.5)
+
+
+ pfit = Parameters()
+ pfit.add(name='amp_g', value=10)
+ pfit.add(name='cen_g', value=9)
+ pfit.add(name='wid_g', value=1)
+
+ pfit.add(name='amp_tot', value=20)
+ pfit.add(name='amp_l', expr='amp_tot - amp_g')
+ pfit.add(name='cen_l', expr='1.5+cen_g')
+ pfit.add(name='wid_l', expr='2*wid_g')
+
+ pfit.add(name='line_slope', value=0.0)
+ pfit.add(name='line_off', value=0.0)
+
+ sigma = 0.021 # estimate of data error (for all data points)
+
+ myfit = Minimizer(residual, pfit,
+ fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
+ scale_covar=True)
+
+ myfit.prepare_fit()
+ init = residual(myfit.params, x)
+
+ result = myfit.leastsq()
+
+ print(' Nfev = ', result.nfev)
+ print( result.chisqr, result.redchi, result.nfree)
+
+ report_fit(result.params)
+ pfit= result.params
+ fit = residual(result.params, x)
+ assert(pfit['cen_l'].value == 1.5 + pfit['cen_g'].value)
+ assert(pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value)
+ assert(pfit['wid_l'].value == 2 * pfit['wid_g'].value)
+
+def test_constraints2():
+ """add a user-defined function to symbol table"""
+ def residual(pars, x, sigma=None, data=None):
+ yg = gaussian(x, pars['amp_g'].value,
+ pars['cen_g'].value, pars['wid_g'].value)
+ yl = lorentzian(x, pars['amp_l'].value,
+ pars['cen_l'].value, pars['wid_l'].value)
+
+ slope = pars['line_slope'].value
+ offset = pars['line_off'].value
+ model = yg + yl + offset + x * slope
+ if data is None:
+ return model
+ if sigma is None:
+ return (model - data)
+ return (model - data)/sigma
+
+
+ n = 601
+ xmin = 0.
+ xmax = 20.0
+ x = linspace(xmin, xmax, n)
+
+ data = (gaussian(x, 21, 8.1, 1.2) +
+ lorentzian(x, 10, 9.6, 2.4) +
+ random.normal(scale=0.23, size=n) +
+ x*0.5)
+
+ pfit = Parameters()
+ pfit.add(name='amp_g', value=10)
+ pfit.add(name='cen_g', value=9)
+ pfit.add(name='wid_g', value=1)
+
+ pfit.add(name='amp_tot', value=20)
+ pfit.add(name='amp_l', expr='amp_tot - amp_g')
+ pfit.add(name='cen_l', expr='1.5+cen_g')
+ pfit.add(name='line_slope', value=0.0)
+ pfit.add(name='line_off', value=0.0)
+
+ sigma = 0.021 # estimate of data error (for all data points)
+
+ myfit = Minimizer(residual, pfit,
+ fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
+ scale_covar=True)
+
+ def width_func(wpar):
+ """ """
+ return 2*wpar
+
+ myfit.params._asteval.symtable['wfun'] = width_func
+
+ try:
+ myfit.params.add(name='wid_l', expr='wfun(wid_g)')
+ except:
+ assert(False)
+
+ result = myfit.leastsq()
+
+ print(' Nfev = ', result.nfev)
+ print( result.chisqr, result.redchi, result.nfree)
+ report_fit(result.params)
+ pfit= result.params
+ fit = residual(result.params, x)
+ assert(pfit['cen_l'].value == 1.5 + pfit['cen_g'].value)
+ assert(pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value)
+ assert(pfit['wid_l'].value == 2 * pfit['wid_g'].value)
+
+
+def test_constraints3():
+ """test a constraint with simple function call"""
+ x = [1723, 1773, 1823, 1523, 1773, 1033.03078,
+ 1042.98077, 1047.90937, 1053.95899, 1057.94906,
+ 1063.13788, 1075.74218, 1086.03102]
+ y = [0.79934, -0.31876, -0.46852, 0.05, -0.21,
+ 11.1708, 10.31844, 9.73069, 9.21319, 9.12457,
+ 9.05243, 8.66407, 8.29664]
+
+ def VFT(T, ninf=-3, A=5e3, T0=800):
+ return ninf + A/(T-T0)
+
+ vftModel = Model(VFT)
+ vftModel.set_param_hint('D', vary=False, expr=r'A*log(10)/T0')
+ result = vftModel.fit(y, T=x)
+ assert(result.params['A'].value > 2600.0)
+ assert(result.params['A'].value < 2650.0)
+ assert(result.params['D'].value > 7.0)
+ assert(result.params['D'].value < 7.5)
+
+if __name__ == '__main__':
+ test_constraints1()
+ test_constraints2()
+ test_constraints3()
diff --git a/tests/test_algebraic_constraint2.py b/tests/test_algebraic_constraint2.py
index 9b4cd88..45a9b6a 100644
--- a/tests/test_algebraic_constraint2.py
+++ b/tests/test_algebraic_constraint2.py
@@ -1,103 +1,103 @@
-from numpy import linspace, zeros, sin, exp, random, sqrt, pi, sign
-from lmfit import Parameters, Parameter, Minimizer
-from lmfit.lineshapes import gaussian, lorentzian, pvoigt
-from lmfit.printfuncs import report_fit
-import sys
-
-
-# Turn off plotting if run by nosetests.
-WITHPLOT = True
-for arg in sys.argv:
- if 'nose' in arg:
- WITHPLOT = False
-
-if WITHPLOT:
- try:
- import matplotlib
- import pylab
- except ImportError:
- WITHPLOT = False
-
-
-def test_constraints(with_plot=True):
- with_plot = with_plot and WITHPLOT
-
- def residual(pars, x, sigma=None, data=None):
- yg = gaussian(x, pars['amp_g'].value,
- pars['cen_g'].value, pars['wid_g'].value)
- yl = lorentzian(x, pars['amp_l'].value,
- pars['cen_l'].value, pars['wid_l'].value)
-
- slope = pars['line_slope'].value
- offset = pars['line_off'].value
- model = yg + yl + offset + x * slope
- if data is None:
- return model
- if sigma is None:
- return (model - data)
- return (model - data) / sigma
-
-
- n = 201
- xmin = 0.
- xmax = 20.0
- x = linspace(xmin, xmax, n)
-
- data = (gaussian(x, 21, 8.1, 1.2) +
- lorentzian(x, 10, 9.6, 2.4) +
- random.normal(scale=0.23, size=n) +
- x*0.5)
-
- if with_plot:
- pylab.plot(x, data, 'r+')
-
- pfit = Parameters()
- pfit.add(name='amp_g', value=10)
- pfit.add(name='cen_g', value=9)
- pfit.add(name='wid_g', value=1)
-
- pfit.add(name='amp_tot', value=20)
- pfit.add(name='amp_l', expr='amp_tot - amp_g')
- pfit.add(name='cen_l', expr='1.5+cen_g')
- pfit.add(name='wid_l', expr='2*wid_g')
-
- pfit.add(name='line_slope', value=0.0)
- pfit.add(name='line_off', value=0.0)
-
- sigma = 0.021 # estimate of data error (for all data points)
-
- myfit = Minimizer(residual, pfit,
- fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
- scale_covar=True)
-
- myfit.prepare_fit()
- init = residual(myfit.params, x)
-
- result = myfit.leastsq()
-
- print(' Nfev = ', result.nfev)
- print( result.chisqr, result.redchi, result.nfree)
-
- report_fit(result.params, min_correl=0.3)
-
- fit = residual(result.params, x)
- if with_plot:
- pylab.plot(x, fit, 'b-')
- assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value)
- assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value)
- assert(result.params['wid_l'].value == 2 * result.params['wid_g'].value)
-
- # now, change fit slightly and re-run
- myfit.params['wid_l'].expr = '1.25*wid_g'
- result = myfit.leastsq()
- report_fit(result.params, min_correl=0.4)
- fit2 = residual(result.params, x)
- if with_plot:
- pylab.plot(x, fit2, 'k')
- pylab.show()
-
- assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value)
- assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value)
- assert(result.params['wid_l'].value == 1.25 * result.params['wid_g'].value)
-
-test_constraints()
+from numpy import linspace, zeros, sin, exp, random, sqrt, pi, sign
+from lmfit import Parameters, Parameter, Minimizer
+from lmfit.lineshapes import gaussian, lorentzian, pvoigt
+from lmfit.printfuncs import report_fit
+import sys
+
+
+# Turn off plotting if run by nosetests.
+WITHPLOT = True
+for arg in sys.argv:
+ if 'nose' in arg:
+ WITHPLOT = False
+
+if WITHPLOT:
+ try:
+ import matplotlib
+ import pylab
+ except ImportError:
+ WITHPLOT = False
+
+
+def test_constraints(with_plot=True):
+ with_plot = with_plot and WITHPLOT
+
+ def residual(pars, x, sigma=None, data=None):
+ yg = gaussian(x, pars['amp_g'].value,
+ pars['cen_g'].value, pars['wid_g'].value)
+ yl = lorentzian(x, pars['amp_l'].value,
+ pars['cen_l'].value, pars['wid_l'].value)
+
+ slope = pars['line_slope'].value
+ offset = pars['line_off'].value
+ model = yg + yl + offset + x * slope
+ if data is None:
+ return model
+ if sigma is None:
+ return (model - data)
+ return (model - data) / sigma
+
+
+ n = 201
+ xmin = 0.
+ xmax = 20.0
+ x = linspace(xmin, xmax, n)
+
+ data = (gaussian(x, 21, 8.1, 1.2) +
+ lorentzian(x, 10, 9.6, 2.4) +
+ random.normal(scale=0.23, size=n) +
+ x*0.5)
+
+ if with_plot:
+ pylab.plot(x, data, 'r+')
+
+ pfit = Parameters()
+ pfit.add(name='amp_g', value=10)
+ pfit.add(name='cen_g', value=9)
+ pfit.add(name='wid_g', value=1)
+
+ pfit.add(name='amp_tot', value=20)
+ pfit.add(name='amp_l', expr='amp_tot - amp_g')
+ pfit.add(name='cen_l', expr='1.5+cen_g')
+ pfit.add(name='wid_l', expr='2*wid_g')
+
+ pfit.add(name='line_slope', value=0.0)
+ pfit.add(name='line_off', value=0.0)
+
+ sigma = 0.021 # estimate of data error (for all data points)
+
+ myfit = Minimizer(residual, pfit,
+ fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
+ scale_covar=True)
+
+ myfit.prepare_fit()
+ init = residual(myfit.params, x)
+
+ result = myfit.leastsq()
+
+ print(' Nfev = ', result.nfev)
+ print( result.chisqr, result.redchi, result.nfree)
+
+ report_fit(result.params, min_correl=0.3)
+
+ fit = residual(result.params, x)
+ if with_plot:
+ pylab.plot(x, fit, 'b-')
+ assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value)
+ assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value)
+ assert(result.params['wid_l'].value == 2 * result.params['wid_g'].value)
+
+ # now, change fit slightly and re-run
+ myfit.params['wid_l'].expr = '1.25*wid_g'
+ result = myfit.leastsq()
+ report_fit(result.params, min_correl=0.4)
+ fit2 = residual(result.params, x)
+ if with_plot:
+ pylab.plot(x, fit2, 'k')
+ pylab.show()
+
+ assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value)
+ assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value)
+ assert(result.params['wid_l'].value == 1.25 * result.params['wid_g'].value)
+
+test_constraints()
diff --git a/tests/test_basicfit.py b/tests/test_basicfit.py
index bcad50c..98b6338 100644
--- a/tests/test_basicfit.py
+++ b/tests/test_basicfit.py
@@ -1,47 +1,47 @@
-import numpy as np
-from lmfit import minimize, Parameters, Parameter, report_fit
-from lmfit_testutils import assert_paramval, assert_paramattr
-
-
-def test_basic():
- # create data to be fitted
- x = np.linspace(0, 15, 301)
- data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) +
- np.random.normal(size=len(x), scale=0.2) )
-
- # define objective function: returns the array to be minimized
- def fcn2min(params, x, data):
- """ model decaying sine wave, subtract data"""
- amp = params['amp'].value
- shift = params['shift'].value
- omega = params['omega'].value
- decay = params['decay'].value
-
- model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay)
- return model - data
-
- # create a set of Parameters
- params = Parameters()
- params.add('amp', value= 10, min=0)
- params.add('decay', value= 0.1)
- params.add('shift', value= 0.0, min=-np.pi/2., max=np.pi/2)
- params.add('omega', value= 3.0)
-
- # do fit, here with leastsq model
- result = minimize(fcn2min, params, args=(x, data))
-
- # calculate final result
- final = data + result.residual
-
- # report_fit(result)
-
- assert(result.nfev > 5)
- assert(result.nfev < 500)
- assert(result.chisqr > 1)
- assert(result.nvarys == 4)
- assert_paramval(result.params['amp'], 5.03, tol=0.05)
- assert_paramval(result.params['omega'], 2.0, tol=0.05)
-
-
-if __name__ == '__main__':
- test_basic()
+import numpy as np
+from lmfit import minimize, Parameters, Parameter, report_fit
+from lmfit_testutils import assert_paramval, assert_paramattr
+
+
+def test_basic():
+ # create data to be fitted
+ x = np.linspace(0, 15, 301)
+ data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) +
+ np.random.normal(size=len(x), scale=0.2) )
+
+ # define objective function: returns the array to be minimized
+ def fcn2min(params, x, data):
+ """ model decaying sine wave, subtract data"""
+ amp = params['amp'].value
+ shift = params['shift'].value
+ omega = params['omega'].value
+ decay = params['decay'].value
+
+ model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay)
+ return model - data
+
+ # create a set of Parameters
+ params = Parameters()
+ params.add('amp', value= 10, min=0)
+ params.add('decay', value= 0.1)
+ params.add('shift', value= 0.0, min=-np.pi/2., max=np.pi/2)
+ params.add('omega', value= 3.0)
+
+ # do fit, here with leastsq model
+ result = minimize(fcn2min, params, args=(x, data))
+
+ # calculate final result
+ final = data + result.residual
+
+ # report_fit(result)
+
+ assert(result.nfev > 5)
+ assert(result.nfev < 500)
+ assert(result.chisqr > 1)
+ assert(result.nvarys == 4)
+ assert_paramval(result.params['amp'], 5.03, tol=0.05)
+ assert_paramval(result.params['omega'], 2.0, tol=0.05)
+
+
+if __name__ == '__main__':
+ test_basic()
diff --git a/tests/test_bounded_jacobian.py b/tests/test_bounded_jacobian.py
index a8fc2f4..810a505 100644
--- a/tests/test_bounded_jacobian.py
+++ b/tests/test_bounded_jacobian.py
@@ -1,43 +1,43 @@
-from lmfit import Parameters, minimize, fit_report
-from lmfit_testutils import assert_paramval, assert_paramattr
-
-import numpy as np
-
-
-def test_bounded_jacobian():
- pars = Parameters()
- pars.add('x0', value=2.0)
- pars.add('x1', value=2.0, min=1.5)
-
- global jac_count
-
- jac_count = 0
-
- def resid(params):
- x0 = params['x0'].value
- x1 = params['x1'].value
- return np.array([10 * (x1 - x0*x0), 1-x0])
-
- def jac(params):
- global jac_count
- jac_count += 1
- x0 = params['x0'].value
- return np.array([[-20*x0, 10], [-1, 0]])
-
- out0 = minimize(resid, pars, Dfun=None)
-
- assert_paramval(out0.params['x0'], 1.2243, tol=0.02)
- assert_paramval(out0.params['x1'], 1.5000, tol=0.02)
- assert(jac_count == 0)
-
- out1 = minimize(resid, pars, Dfun=jac)
-
- assert_paramval(out1.params['x0'], 1.2243, tol=0.02)
- assert_paramval(out1.params['x1'], 1.5000, tol=0.02)
- assert(jac_count > 5)
-
- print(fit_report(out1, show_correl=True))
-
-
-if __name__ == '__main__':
- test_bounded_jacobian()
+from lmfit import Parameters, minimize, fit_report
+from lmfit_testutils import assert_paramval, assert_paramattr
+
+import numpy as np
+
+
+def test_bounded_jacobian():
+ pars = Parameters()
+ pars.add('x0', value=2.0)
+ pars.add('x1', value=2.0, min=1.5)
+
+ global jac_count
+
+ jac_count = 0
+
+ def resid(params):
+ x0 = params['x0'].value
+ x1 = params['x1'].value
+ return np.array([10 * (x1 - x0*x0), 1-x0])
+
+ def jac(params):
+ global jac_count
+ jac_count += 1
+ x0 = params['x0'].value
+ return np.array([[-20*x0, 10], [-1, 0]])
+
+ out0 = minimize(resid, pars, Dfun=None)
+
+ assert_paramval(out0.params['x0'], 1.2243, tol=0.02)
+ assert_paramval(out0.params['x1'], 1.5000, tol=0.02)
+ assert(jac_count == 0)
+
+ out1 = minimize(resid, pars, Dfun=jac)
+
+ assert_paramval(out1.params['x0'], 1.2243, tol=0.02)
+ assert_paramval(out1.params['x1'], 1.5000, tol=0.02)
+ assert(jac_count > 5)
+
+ print(fit_report(out1, show_correl=True))
+
+
+if __name__ == '__main__':
+ test_bounded_jacobian()
diff --git a/tests/test_bounds.py b/tests/test_bounds.py
index c23ee94..99c962d 100644
--- a/tests/test_bounds.py
+++ b/tests/test_bounds.py
@@ -1,54 +1,54 @@
-from lmfit import Parameters, minimize, fit_report
-from lmfit_testutils import assert_paramval, assert_paramattr
-
-from numpy import linspace, zeros, sin, exp, random, pi, sign
-
-def test_bounds():
- p_true = Parameters()
- p_true.add('amp', value=14.0)
- p_true.add('period', value=5.4321)
- p_true.add('shift', value=0.12345)
- p_true.add('decay', value=0.01000)
-
- def residual(pars, x, data=None):
- amp = pars['amp'].value
- per = pars['period'].value
- shift = pars['shift'].value
- decay = pars['decay'].value
-
- if abs(shift) > pi/2:
- shift = shift - sign(shift)*pi
-
- model = amp*sin(shift + x/per) * exp(-x*x*decay*decay)
- if data is None:
- return model
- return (model - data)
-
- n = 1500
- xmin = 0.
- xmax = 250.0
- random.seed(0)
- noise = random.normal(scale=2.80, size=n)
- x = linspace(xmin, xmax, n)
- data = residual(p_true, x) + noise
-
- fit_params = Parameters()
- fit_params.add('amp', value=13.0, max=20, min=0.0)
- fit_params.add('period', value=2, max=10)
- fit_params.add('shift', value=0.0, max=pi/2., min=-pi/2.)
- fit_params.add('decay', value=0.02, max=0.10, min=0.00)
-
- out = minimize(residual, fit_params, args=(x,), kws={'data':data})
-
- fit = residual(out.params, x)
-
- assert(out.nfev > 10)
- assert(out.nfree > 50)
- assert(out.chisqr > 1.0)
-
- print(fit_report(out, show_correl=True, modelpars=p_true))
- assert_paramval(out.params['decay'], 0.01, tol=1.e-2)
- assert_paramval(out.params['shift'], 0.123, tol=1.e-2)
-
-if __name__ == '__main__':
- test_bounds()
+from lmfit import Parameters, minimize, fit_report
+from lmfit_testutils import assert_paramval, assert_paramattr
+
+from numpy import linspace, zeros, sin, exp, random, pi, sign
+
+def test_bounds():
+ p_true = Parameters()
+ p_true.add('amp', value=14.0)
+ p_true.add('period', value=5.4321)
+ p_true.add('shift', value=0.12345)
+ p_true.add('decay', value=0.01000)
+
+ def residual(pars, x, data=None):
+ amp = pars['amp'].value
+ per = pars['period'].value
+ shift = pars['shift'].value
+ decay = pars['decay'].value
+
+ if abs(shift) > pi/2:
+ shift = shift - sign(shift)*pi
+
+ model = amp*sin(shift + x/per) * exp(-x*x*decay*decay)
+ if data is None:
+ return model
+ return (model - data)
+
+ n = 1500
+ xmin = 0.
+ xmax = 250.0
+ random.seed(0)
+ noise = random.normal(scale=2.80, size=n)
+ x = linspace(xmin, xmax, n)
+ data = residual(p_true, x) + noise
+
+ fit_params = Parameters()
+ fit_params.add('amp', value=13.0, max=20, min=0.0)
+ fit_params.add('period', value=2, max=10)
+ fit_params.add('shift', value=0.0, max=pi/2., min=-pi/2.)
+ fit_params.add('decay', value=0.02, max=0.10, min=0.00)
+
+ out = minimize(residual, fit_params, args=(x,), kws={'data':data})
+
+ fit = residual(out.params, x)
+
+ assert(out.nfev > 10)
+ assert(out.nfree > 50)
+ assert(out.chisqr > 1.0)
+
+ print(fit_report(out, show_correl=True, modelpars=p_true))
+ assert_paramval(out.params['decay'], 0.01, tol=1.e-2)
+ assert_paramval(out.params['shift'], 0.123, tol=1.e-2)
+
+if __name__ == '__main__':
+ test_bounds()
diff --git a/tests/test_confidence.py b/tests/test_confidence.py
index 7d90d00..2b5d290 100644
--- a/tests/test_confidence.py
+++ b/tests/test_confidence.py
@@ -1,44 +1,88 @@
-import numpy as np
-from numpy.testing import assert_allclose
-
-import lmfit
-from lmfit_testutils import assert_paramval
-
-def residual(params, x, data):
- a = params['a'].value
- b = params['b'].value
- return data - 1.0/(a*x)+b
-
-def test_confidence1():
- x = np.linspace(0.3,10,100)
- np.random.seed(0)
-
- y = 1/(0.1*x)+2+0.1*np.random.randn(x.size)
-
- pars = lmfit.Parameters()
- pars.add_many(('a', 0.1), ('b', 1))
-
- minimizer = lmfit.Minimizer(residual, pars, fcn_args=(x, y) )
- out = minimizer.leastsq()
- # lmfit.report_fit(out)
-
- assert(out.nfev > 5)
- assert(out.nfev < 500)
- assert(out.chisqr < 3.0)
- assert(out.nvarys == 2)
-
- assert_paramval(out.params['a'], 0.1, tol=0.1)
- assert_paramval(out.params['b'], -2.0, tol=0.1)
-
- ci = lmfit.conf_interval(minimizer, out)
- assert_allclose(ci['b'][0][0], 0.997, rtol=0.01)
- assert_allclose(ci['b'][0][1], -2.022, rtol=0.01)
- assert_allclose(ci['b'][2][0], 0.674, rtol=0.01)
- assert_allclose(ci['b'][2][1], -1.997, rtol=0.01)
- assert_allclose(ci['b'][5][0], 0.95, rtol=0.01)
- assert_allclose(ci['b'][5][1], -1.96, rtol=0.01)
-
- # lmfit.printfuncs.report_ci(ci)
-
-if __name__ == '__main__':
- test_confidence1()
+import numpy as np
+from numpy.testing import assert_allclose
+
+import lmfit
+from lmfit_testutils import assert_paramval
+
+def residual(params, x, data):
+ a = params['a'].value
+ b = params['b'].value
+ return data - 1.0/(a*x)+b
+
+def residual2(params, x, data):
+ a = params['a'].value
+ b = params['b'].value
+ c = params['c'].value
+ return data - c/(a*x)+b
+
+def test_confidence1():
+ x = np.linspace(0.3,10,100)
+ np.random.seed(0)
+
+ y = 1/(0.1*x)+2+0.1*np.random.randn(x.size)
+
+ pars = lmfit.Parameters()
+ pars.add_many(('a', 0.1), ('b', 1))
+
+ minimizer = lmfit.Minimizer(residual, pars, fcn_args=(x, y) )
+ out = minimizer.leastsq()
+ # lmfit.report_fit(out)
+
+ assert(out.nfev > 5)
+ assert(out.nfev < 500)
+ assert(out.chisqr < 3.0)
+ assert(out.nvarys == 2)
+
+ assert_paramval(out.params['a'], 0.1, tol=0.1)
+ assert_paramval(out.params['b'], -2.0, tol=0.1)
+
+ ci = lmfit.conf_interval(minimizer, out)
+ assert_allclose(ci['b'][0][0], 0.997, rtol=0.01)
+ assert_allclose(ci['b'][0][1], -2.022, rtol=0.01)
+ assert_allclose(ci['b'][2][0], 0.674, rtol=0.01)
+ assert_allclose(ci['b'][2][1], -1.997, rtol=0.01)
+ assert_allclose(ci['b'][5][0], 0.95, rtol=0.01)
+ assert_allclose(ci['b'][5][1], -1.96, rtol=0.01)
+
+ # lmfit.printfuncs.report_ci(ci)
+
+
+def test_confidence2():
+ x = np.linspace(0.3,10,100)
+ np.random.seed(0)
+
+ y = 1/(0.1*x)+2+0.1*np.random.randn(x.size)
+
+ pars = lmfit.Parameters()
+ pars.add_many(('a', 0.1), ('b', 1), ('c', 1.0))
+ pars['a'].max = 0.25
+ pars['a'].min = 0.00
+ pars['a'].value = 0.2
+ pars['c'].vary = False
+
+ minimizer = lmfit.Minimizer(residual2, pars, fcn_args=(x, y) )
+ out = minimizer.minimize(method='nelder')
+ out = minimizer.minimize(method='leastsq', params=out.params)
+ # lmfit.report_fit(out)
+
+ assert(out.nfev > 5)
+ assert(out.nfev < 500)
+ assert(out.chisqr < 3.0)
+ assert(out.nvarys == 2)
+
+ assert_paramval(out.params['a'], 0.1, tol=0.1)
+ assert_paramval(out.params['b'], -2.0, tol=0.1)
+
+ ci = lmfit.conf_interval(minimizer, out)
+ assert_allclose(ci['b'][0][0], 0.997, rtol=0.01)
+ assert_allclose(ci['b'][0][1], -2.022, rtol=0.01)
+ assert_allclose(ci['b'][2][0], 0.674, rtol=0.01)
+ assert_allclose(ci['b'][2][1], -1.997, rtol=0.01)
+ assert_allclose(ci['b'][5][0], 0.95, rtol=0.01)
+ assert_allclose(ci['b'][5][1], -1.96, rtol=0.01)
+
+ lmfit.printfuncs.report_ci(ci)
+
+if __name__ == '__main__':
+ test_confidence1()
+ test_confidence2()
diff --git a/tests/test_copy_params.py b/tests/test_copy_params.py
index d68387b..e17aa18 100644
--- a/tests/test_copy_params.py
+++ b/tests/test_copy_params.py
@@ -1,36 +1,36 @@
-import numpy as np
-from lmfit import Parameters, minimize, report_fit
-
-def get_data():
- x = np.arange(0, 1, 0.01)
- y1 = 1.5*np.exp(0.9*x) + np.random.normal(scale=0.001, size=len(x))
- y2 = 2.0 + x + 1/2.*x**2 +1/3.*x**3
- y2 = y2 + np.random.normal(scale=0.001, size=len(x))
- return x, y1, y2
-
-def residual(params, x, data):
- a = params['a'].value
- b = params['b'].value
-
- model = a*np.exp(b*x)
- return (data-model)
-
-def test_copy_params():
- x, y1, y2 = get_data()
-
- params = Parameters()
- params.add('a', value = 2.0)
- params.add('b', value = 2.0)
-
- # fit to first data set
- out1 = minimize(residual, params, args=(x, y1))
-
- # fit to second data set
- out2 = minimize(residual, params, args=(x, y2))
-
- adiff = out1.params['a'].value - out2.params['a'].value
- bdiff = out1.params['b'].value - out2.params['b'].value
-
- assert(abs(adiff) > 1.e-2)
- assert(abs(bdiff) > 1.e-2)
-
+import numpy as np
+from lmfit import Parameters, minimize, report_fit
+
+def get_data():
+ x = np.arange(0, 1, 0.01)
+ y1 = 1.5*np.exp(0.9*x) + np.random.normal(scale=0.001, size=len(x))
+ y2 = 2.0 + x + 1/2.*x**2 +1/3.*x**3
+ y2 = y2 + np.random.normal(scale=0.001, size=len(x))
+ return x, y1, y2
+
+def residual(params, x, data):
+ a = params['a'].value
+ b = params['b'].value
+
+ model = a*np.exp(b*x)
+ return (data-model)
+
+def test_copy_params():
+ x, y1, y2 = get_data()
+
+ params = Parameters()
+ params.add('a', value = 2.0)
+ params.add('b', value = 2.0)
+
+ # fit to first data set
+ out1 = minimize(residual, params, args=(x, y1))
+
+ # fit to second data set
+ out2 = minimize(residual, params, args=(x, y2))
+
+ adiff = out1.params['a'].value - out2.params['a'].value
+ bdiff = out1.params['b'].value - out2.params['b'].value
+
+ assert(abs(adiff) > 1.e-2)
+ assert(abs(bdiff) > 1.e-2)
+
diff --git a/tests/test_default_kws.py b/tests/test_default_kws.py
index 93a1c8f..8ab835f 100644
--- a/tests/test_default_kws.py
+++ b/tests/test_default_kws.py
@@ -1,24 +1,24 @@
-import numpy as np
-from nose.tools import assert_true
-from lmfit.lineshapes import gaussian
-from lmfit.models import GaussianModel
-
-
-def test_default_inputs_gauss():
-
- area = 1
- cen = 0
- std = 0.2
- x = np.arange(-3, 3, 0.01)
- y = gaussian(x, area, cen, std)
-
- g = GaussianModel()
-
- fit_option1 = {'maxfev': 5000, 'xtol': 1e-2}
- result1 = g.fit(y, x=x, amplitude=1, center=0, sigma=0.5, fit_kws=fit_option1)
-
- fit_option2 = {'maxfev': 5000, 'xtol': 1e-6}
- result2 = g.fit(y, x=x, amplitude=1, center=0, sigma=0.5, fit_kws=fit_option2)
-
- assert_true(result1.values!=result2.values)
- return
+import numpy as np
+from nose.tools import assert_true
+from lmfit.lineshapes import gaussian
+from lmfit.models import GaussianModel
+
+
+def test_default_inputs_gauss():
+
+ area = 1
+ cen = 0
+ std = 0.2
+ x = np.arange(-3, 3, 0.01)
+ y = gaussian(x, area, cen, std)
+
+ g = GaussianModel()
+
+ fit_option1 = {'maxfev': 5000, 'xtol': 1e-2}
+ result1 = g.fit(y, x=x, amplitude=1, center=0, sigma=0.5, fit_kws=fit_option1)
+
+ fit_option2 = {'maxfev': 5000, 'xtol': 1e-6}
+ result2 = g.fit(y, x=x, amplitude=1, center=0, sigma=0.5, fit_kws=fit_option2)
+
+ assert_true(result1.values!=result2.values)
+ return
diff --git a/tests/test_itercb.py b/tests/test_itercb.py
index cefcc5d..f77eb48 100644
--- a/tests/test_itercb.py
+++ b/tests/test_itercb.py
@@ -1,29 +1,29 @@
-import numpy as np
-from lmfit import Parameters, minimize, report_fit
-from lmfit.models import LinearModel, GaussianModel
-from lmfit.lineshapes import gaussian
-
-def per_iteration(pars, iter, resid, *args, **kws):
- """iteration callback, will abort at iteration 23
- """
- # print( iter, ', '.join(["%s=%.4f" % (p.name, p.value) for p in pars.values()]))
- return iter == 23
-
-def test_itercb():
- x = np.linspace(0, 20, 401)
- y = gaussian(x, amplitude=24.56, center=7.6543, sigma=1.23)
- y = y - .20*x + 3.333 + np.random.normal(scale=0.23, size=len(x))
- mod = GaussianModel(prefix='peak_') + LinearModel(prefix='bkg_')
-
- pars = mod.make_params(peak_amplitude=21.0,
- peak_center=7.0,
- peak_sigma=2.0,
- bkg_intercept=2,
- bkg_slope=0.0)
-
- out = mod.fit(y, pars, x=x, iter_cb=per_iteration)
-
- assert(out.nfev == 23)
- assert(out.aborted)
- assert(not out.errorbars)
- assert(not out.success)
+import numpy as np
+from lmfit import Parameters, minimize, report_fit
+from lmfit.models import LinearModel, GaussianModel
+from lmfit.lineshapes import gaussian
+
+def per_iteration(pars, iter, resid, *args, **kws):
+ """iteration callback, will abort at iteration 23
+ """
+ # print( iter, ', '.join(["%s=%.4f" % (p.name, p.value) for p in pars.values()]))
+ return iter == 23
+
+def test_itercb():
+ x = np.linspace(0, 20, 401)
+ y = gaussian(x, amplitude=24.56, center=7.6543, sigma=1.23)
+ y = y - .20*x + 3.333 + np.random.normal(scale=0.23, size=len(x))
+ mod = GaussianModel(prefix='peak_') + LinearModel(prefix='bkg_')
+
+ pars = mod.make_params(peak_amplitude=21.0,
+ peak_center=7.0,
+ peak_sigma=2.0,
+ bkg_intercept=2,
+ bkg_slope=0.0)
+
+ out = mod.fit(y, pars, x=x, iter_cb=per_iteration)
+
+ assert(out.nfev == 23)
+ assert(out.aborted)
+ assert(not out.errorbars)
+ assert(not out.success)
diff --git a/tests/test_manypeaks_speed.py b/tests/test_manypeaks_speed.py
index 4f870ac..c756936 100644
--- a/tests/test_manypeaks_speed.py
+++ b/tests/test_manypeaks_speed.py
@@ -1,37 +1,37 @@
-#
-# test speed of building complex model
-#
-import time
-import sys
-import numpy as np
-from lmfit import Model
-from lmfit.lineshapes import gaussian
-from copy import deepcopy
-
-
-sys.setrecursionlimit(2000)
-
-def test_manypeaks_speed():
- x = np.linspace( -5, 5, 251)
- model = None
- t0 = time.time()
- for i in np.arange(500):
- g = Model(gaussian, prefix='g%i_' % i)
- if model is None:
- model = g
- else:
- model += g
- t1 = time.time()
- pars = model.make_params()
- t2 = time.time()
- cpars = deepcopy(pars)
- t3 = time.time()
-
- # these are very conservative tests that
- # should be satisfied on nearly any machine
- assert((t3-t2) < 0.5)
- assert((t2-t1) < 0.5)
- assert((t1-t0) < 5.0)
-
-if __name__ == '__main__':
- test_manypeaks_speed()
+#
+# test speed of building complex model
+#
+import time
+import sys
+import numpy as np
+from lmfit import Model
+from lmfit.lineshapes import gaussian
+from copy import deepcopy
+
+
+sys.setrecursionlimit(2000)
+
+def test_manypeaks_speed():
+ x = np.linspace( -5, 5, 251)
+ model = None
+ t0 = time.time()
+ for i in np.arange(500):
+ g = Model(gaussian, prefix='g%i_' % i)
+ if model is None:
+ model = g
+ else:
+ model += g
+ t1 = time.time()
+ pars = model.make_params()
+ t2 = time.time()
+ cpars = deepcopy(pars)
+ t3 = time.time()
+
+ # these are very conservative tests that
+ # should be satisfied on nearly any machine
+ assert((t3-t2) < 0.5)
+ assert((t2-t1) < 0.5)
+ assert((t1-t0) < 5.0)
+
+if __name__ == '__main__':
+ test_manypeaks_speed()
diff --git a/tests/test_model.py b/tests/test_model.py
index bcc389d..9cede12 100644
--- a/tests/test_model.py
+++ b/tests/test_model.py
@@ -1,503 +1,585 @@
-import unittest
-import warnings
-import nose
-from numpy.testing import assert_allclose
-from numpy.testing.decorators import knownfailureif
-import numpy as np
-
-from lmfit import Model, Parameter, models
-from lmfit.lineshapes import gaussian
-
-def assert_results_close(actual, desired, rtol=1e-03, atol=1e-03,
- err_msg='', verbose=True):
- for param_name, value in desired.items():
- assert_allclose(actual[param_name], value, rtol, atol, err_msg, verbose)
-
-def _skip_if_no_pandas():
- try:
- import pandas
- except ImportError:
- raise nose.SkipTest("Skipping tests that require pandas.")
-
-
-class CommonTests(object):
- # to be subclassed for testing predefined models
-
- def setUp(self):
- np.random.seed(1)
- self.noise = 0.0001*np.random.randn(*self.x.shape)
- # Some Models need args (e.g., polynomial order), and others don't.
- try:
- args = self.args
- except AttributeError:
- self.model = self.model_constructor()
- self.model_drop = self.model_constructor(missing='drop')
- self.model_raise = self.model_constructor(missing='raise')
- self.model_explicit_var = self.model_constructor(['x'])
- func = self.model.func
- else:
- self.model = self.model_constructor(*args)
- self.model_drop = self.model_constructor(*args, missing='drop')
- self.model_raise = self.model_constructor(*args, missing='raise')
- self.model_explicit_var = self.model_constructor(
- *args, independent_vars=['x'])
- func = self.model.func
- self.data = func(x=self.x, **self.true_values()) + self.noise
-
- @property
- def x(self):
- return np.linspace(1, 10, num=1000)
-
- def test_fit(self):
- model = self.model
-
- # Pass Parameters object.
- params = model.make_params(**self.guess())
- result = model.fit(self.data, params, x=self.x)
- assert_results_close(result.values, self.true_values())
-
- # Pass inidividual Parameter objects as kwargs.
- kwargs = {name: p for name, p in params.items()}
- result = self.model.fit(self.data, x=self.x, **kwargs)
- assert_results_close(result.values, self.true_values())
-
- # Pass guess values (not Parameter objects) as kwargs.
- kwargs = {name: p.value for name, p in params.items()}
- result = self.model.fit(self.data, x=self.x, **kwargs)
- assert_results_close(result.values, self.true_values())
-
- def test_explicit_independent_vars(self):
- self.check_skip_independent_vars()
- model = self.model_explicit_var
- pars = model.make_params(**self.guess())
- result = model.fit(self.data, pars, x=self.x)
- assert_results_close(result.values, self.true_values())
-
- def test_fit_with_weights(self):
- model = self.model
-
- # fit without weights
- params = model.make_params(**self.guess())
- out1 = model.fit(self.data, params, x=self.x)
-
- # fit with weights
- weights = 1.0/(0.5 + self.x**2)
- out2 = model.fit(self.data, params, weights=weights, x=self.x)
-
- max_diff = 0.0
- for parname, val1 in out1.values.items():
- val2 = out2.values[parname]
- if max_diff < abs(val1-val2):
- max_diff = abs(val1-val2)
- assert(max_diff > 1.e-8)
-
- def test_result_attributes(self):
- pars = self.model.make_params(**self.guess())
- result = self.model.fit(self.data, pars, x=self.x)
-
- # result.init_values
- assert_results_close(result.values, self.true_values())
- self.assertEqual(result.init_values, self.guess())
-
- # result.init_params
- params = self.model.make_params()
- for param_name, value in self.guess().items():
- params[param_name].value = value
- self.assertEqual(result.init_params, params)
-
- # result.best_fit
- assert_allclose(result.best_fit, self.data, atol=self.noise.max())
-
- # result.init_fit
- init_fit = self.model.func(x=self.x, **self.guess())
- assert_allclose(result.init_fit, init_fit)
-
- # result.model
- self.assertTrue(result.model is self.model)
-
- def test_result_eval(self):
- # Check eval() output against init_fit and best_fit.
- pars = self.model.make_params(**self.guess())
- result = self.model.fit(self.data, pars, x=self.x)
-
- assert_allclose(result.eval(x=self.x, **result.values),
- result.best_fit)
- assert_allclose(result.eval(x=self.x, **result.init_values),
- result.init_fit)
-
- def test_result_eval_custom_x(self):
- self.check_skip_independent_vars()
- pars = self.model.make_params(**self.guess())
- result = self.model.fit(self.data, pars, x=self.x)
-
- # Check that the independent variable is respected.
- short_eval = result.eval(x=np.array([0, 1, 2]), **result.values)
- self.assertEqual(len(short_eval), 3)
-
- def test_data_alignment(self):
- _skip_if_no_pandas()
- from pandas import Series
-
- # Align data and indep var of different lengths using pandas index.
- data = Series(self.data.copy()).iloc[10:-10]
- x = Series(self.x.copy())
-
- model = self.model
- params = model.make_params(**self.guess())
- result = model.fit(data, params, x=x)
- result = model.fit(data, params, x=x)
- assert_results_close(result.values, self.true_values())
-
- # Skip over missing (NaN) values, aligning via pandas index.
- data.iloc[500:510] = np.nan
- result = self.model_drop.fit(data, params, x=x)
- assert_results_close(result.values, self.true_values())
-
- # Raise if any NaN values are present.
- raises = lambda: self.model_raise.fit(data, params, x=x)
- self.assertRaises(ValueError, raises)
-
- def check_skip_independent_vars(self):
- # to be overridden for models that do not accept indep vars
- pass
-
- def test_aic(self):
- model = self.model
-
- # Pass Parameters object.
- params = model.make_params(**self.guess())
- result = model.fit(self.data, params, x=self.x)
- aic = result.aic
- self.assertTrue(aic < 0) # aic must be negative
-
- # Pass extra unused Parameter.
- params.add("unused_param", value=1.0, vary=True)
- result = model.fit(self.data, params, x=self.x)
- aic_extra = result.aic
- self.assertTrue(aic_extra < 0) # aic must be negative
- self.assertTrue(aic < aic_extra) # the extra param should lower the aic
-
-
- def test_bic(self):
- model = self.model
-
- # Pass Parameters object.
- params = model.make_params(**self.guess())
- result = model.fit(self.data, params, x=self.x)
- bic = result.bic
- self.assertTrue(bic < 0) # aic must be negative
-
- # Compare to AIC
- aic = result.aic
- self.assertTrue(aic < bic) # aic should be lower than bic
-
- # Pass extra unused Parameter.
- params.add("unused_param", value=1.0, vary=True)
- result = model.fit(self.data, params, x=self.x)
- bic_extra = result.bic
- self.assertTrue(bic_extra < 0) # bic must be negative
- self.assertTrue(bic < bic_extra) # the extra param should lower the bic
-
-
-class TestUserDefiniedModel(CommonTests, unittest.TestCase):
- # mainly aimed at checking that the API does what it says it does
- # and raises the right exceptions or warnings when things are not right
-
- def setUp(self):
- self.true_values = lambda: dict(amplitude=7.1, center=1.1, sigma=2.40)
- self.guess = lambda: dict(amplitude=5, center=2, sigma=4)
- # return a fresh copy
- self.model_constructor = (
- lambda *args, **kwargs: Model(gaussian, *args, **kwargs))
- super(TestUserDefiniedModel, self).setUp()
-
- @property
- def x(self):
- return np.linspace(-10, 10, num=1000)
-
- def test_lists_become_arrays(self):
- # smoke test
- self.model.fit([1, 2, 3], x=[1, 2, 3], **self.guess())
- self.model.fit([1, 2, None, 3], x=[1, 2, 3, 4], **self.guess())
-
- def test_missing_param_raises_error(self):
-
- # using keyword argument parameters
- guess_missing_sigma = self.guess()
- del guess_missing_sigma['sigma']
- # f = lambda: self.model.fit(self.data, x=self.x, **guess_missing_sigma)
- # self.assertRaises(ValueError, f)
-
- # using Parameters
- params = self.model.make_params()
- for param_name, value in guess_missing_sigma.items():
- params[param_name].value = value
- f = lambda: self.model.fit(self.data, params, x=self.x)
-
- def test_extra_param_issues_warning(self):
- # The function accepts extra params, Model will warn but not raise.
- def flexible_func(x, amplitude, center, sigma, **kwargs):
- return gaussian(x, amplitude, center, sigma)
-
- flexible_model = Model(flexible_func)
- pars = flexible_model.make_params(**self.guess())
- with warnings.catch_warnings(record=True) as w:
- warnings.simplefilter("always")
- flexible_model.fit(self.data, pars, x=self.x, extra=5)
- self.assertTrue(len(w) == 1)
- self.assertTrue(issubclass(w[-1].category, UserWarning))
-
- def test_missing_independent_variable_raises_error(self):
- pars = self.model.make_params(**self.guess())
- f = lambda: self.model.fit(self.data, pars)
- self.assertRaises(KeyError, f)
-
- def test_bounding(self):
- true_values = self.true_values()
- true_values['center'] = 1.3 # as close as it's allowed to get
- pars = self.model.make_params(**self.guess())
- pars['center'].set(value=2, min=1.3)
- result = self.model.fit(self.data, pars, x=self.x)
- assert_results_close(result.values, true_values, rtol=0.05)
-
- def test_vary_false(self):
- true_values = self.true_values()
- true_values['center'] = 1.3
- pars = self.model.make_params(**self.guess())
- pars['center'].set(value=1.3, vary=False)
- result = self.model.fit(self.data, pars, x=self.x)
- assert_results_close(result.values, true_values, rtol=0.05)
-
- # testing model addition...
-
- def test_user_defined_gaussian_plus_constant(self):
- data = self.data + 5.0
- model = self.model + models.ConstantModel()
- guess = self.guess()
- pars = model.make_params(c= 10.1, **guess)
- true_values = self.true_values()
- true_values['c'] = 5.0
-
- result = model.fit(data, pars, x=self.x)
- assert_results_close(result.values, true_values, rtol=0.01, atol=0.01)
-
- def test_model_with_prefix(self):
- # model with prefix of 'a' and 'b'
- mod = models.GaussianModel(prefix='a')
- vals = {'center': 2.45, 'sigma':0.8, 'amplitude':3.15}
- data = gaussian(x=self.x, **vals) + self.noise/3.0
- pars = mod.guess(data, x=self.x)
- self.assertTrue('aamplitude' in pars)
- self.assertTrue('asigma' in pars)
- out = mod.fit(data, pars, x=self.x)
- self.assertTrue(out.params['aamplitude'].value > 2.0)
- self.assertTrue(out.params['acenter'].value > 2.0)
- self.assertTrue(out.params['acenter'].value < 3.0)
-
- mod = models.GaussianModel(prefix='b')
- data = gaussian(x=self.x, **vals) + self.noise/3.0
- pars = mod.guess(data, x=self.x)
- self.assertTrue('bamplitude' in pars)
- self.assertTrue('bsigma' in pars)
-
- def test_change_prefix(self):
- "should fail"
- mod = models.GaussianModel(prefix='b')
- set_prefix_failed = None
- try:
- mod.prefix = 'c'
- set_prefix_failed = False
- except AttributeError:
- set_prefix_failed = True
- except:
- set_prefix_failed = None
- self.assertTrue(set_prefix_failed)
-
-
- def test_sum_of_two_gaussians(self):
- # two user-defined gaussians
- model1 = self.model
- f2 = lambda x, amp, cen, sig: gaussian(x, amplitude=amp, center=cen, sigma=sig)
- model2 = Model(f2)
- values1 = self.true_values()
- values2 = {'cen': 2.45, 'sig':0.8, 'amp':3.15}
-
- data = gaussian(x=self.x, **values1) + f2(x=self.x, **values2) + self.noise/3.0
- model = self.model + model2
- pars = model.make_params()
- pars['sigma'].set(value=2, min=0)
- pars['center'].set(value=1, min=0.2, max=1.8)
- pars['amplitude'].set(value=3, min=0)
- pars['sig'].set(value=1, min=0)
- pars['cen'].set(value=2.4, min=2, max=3.5)
- pars['amp'].set(value=1, min=0)
-
- true_values = dict(list(values1.items()) + list(values2.items()))
- result = model.fit(data, pars, x=self.x)
- assert_results_close(result.values, true_values, rtol=0.01, atol=0.01)
-
- # user-defined models with common parameter names
- # cannot be added, and should raise
- f = lambda: model1 + model1
- self.assertRaises(NameError, f)
-
- # two predefined_gaussians, using suffix to differentiate
- model1 = models.GaussianModel(prefix='g1_')
- model2 = models.GaussianModel(prefix='g2_')
- model = model1 + model2
- true_values = {'g1_center': values1['center'],
- 'g1_amplitude': values1['amplitude'],
- 'g1_sigma': values1['sigma'],
- 'g2_center': values2['cen'],
- 'g2_amplitude': values2['amp'],
- 'g2_sigma': values2['sig']}
- pars = model.make_params()
- pars['g1_sigma'].set(2)
- pars['g1_center'].set(1)
- pars['g1_amplitude'].set(3)
- pars['g2_sigma'].set(1)
- pars['g2_center'].set(2.4)
- pars['g2_amplitude'].set(1)
-
- result = model.fit(data, pars, x=self.x)
- assert_results_close(result.values, true_values, rtol=0.01, atol=0.01)
-
- # without suffix, the names collide and Model should raise
- model1 = models.GaussianModel()
- model2 = models.GaussianModel()
- f = lambda: model1 + model2
- self.assertRaises(NameError, f)
-
- def test_sum_composite_models(self):
- # test components of composite model created adding composite model
- model1 = models.GaussianModel(prefix='g1_')
- model2 = models.GaussianModel(prefix='g2_')
- model3 = models.GaussianModel(prefix='g3_')
- model4 = models.GaussianModel(prefix='g4_')
-
- model_total1 = (model1 + model2) + model3
- for mod in [model1, model2, model3]:
- self.assertTrue(mod in model_total1.components)
-
- model_total2 = model1 + (model2 + model3)
- for mod in [model1, model2, model3]:
- self.assertTrue(mod in model_total2.components)
-
- model_total3 = (model1 + model2) + (model3 + model4)
- for mod in [model1, model2, model3, model4]:
- self.assertTrue(mod in model_total3.components)
-
- def test_composite_has_bestvalues(self):
- # test that a composite model has non-empty best_values
- model1 = models.GaussianModel(prefix='g1_')
- model2 = models.GaussianModel(prefix='g2_')
-
- mod = model1 + model2
- pars = mod.make_params()
-
- values1 = dict(amplitude=7.10, center=1.1, sigma=2.40)
- values2 = dict(amplitude=12.2, center=2.5, sigma=0.5)
- data = gaussian(x=self.x, **values1) + gaussian(x=self.x, **values2) + 0.1*self.noise
-
- pars['g1_sigma'].set(2)
- pars['g1_center'].set(1, max=1.5)
- pars['g1_amplitude'].set(3)
- pars['g2_sigma'].set(1)
- pars['g2_center'].set(2.6, min=2.0)
- pars['g2_amplitude'].set(1)
-
- result = mod.fit(data, params=pars, x=self.x)
-
- self.assertTrue(len(result.best_values) == 6)
-
- self.assertTrue(abs(result.params['g1_amplitude'].value - 7.1) < 0.5)
- self.assertTrue(abs(result.params['g2_amplitude'].value - 12.2) < 0.5)
- self.assertTrue(abs(result.params['g1_center'].value - 1.1) < 0.2)
- self.assertTrue(abs(result.params['g2_center'].value - 2.5) < 0.2)
-
-
- def test_hints_in_composite_models(self):
- # test propagation of hints from base models to composite model
- def func(x, amplitude):
- pass
-
- m1 = Model(func, prefix='p1_')
- m2 = Model(func, prefix='p2_')
-
- m1.set_param_hint('amplitude', value=1)
- m2.set_param_hint('amplitude', value=2)
-
- mx = (m1 + m2)
- params = mx.make_params()
- param_values = {name: p.value for name, p in params.items()}
- self.assertEqual(param_values['p1_amplitude'], 1)
- self.assertEqual(param_values['p2_amplitude'], 2)
-
-
-class TestLinear(CommonTests, unittest.TestCase):
-
- def setUp(self):
- self.true_values = lambda: dict(slope=5, intercept=2)
- self.guess = lambda: dict(slope=10, intercept=6)
- self.model_constructor = models.LinearModel
- super(TestLinear, self).setUp()
-
-
-class TestParabolic(CommonTests, unittest.TestCase):
-
- def setUp(self):
- self.true_values = lambda: dict(a=5, b=2, c=8)
- self.guess = lambda: dict(a=1, b=6, c=3)
- self.model_constructor = models.ParabolicModel
- super(TestParabolic, self).setUp()
-
-
-class TestPolynomialOrder2(CommonTests, unittest.TestCase):
- # class Polynomial constructed with order=2
-
- def setUp(self):
- self.true_values = lambda: dict(c2=5, c1=2, c0=8)
- self.guess = lambda: dict(c1=1, c2=6, c0=3)
- self.model_constructor = models.PolynomialModel
- self.args = (2,)
- super(TestPolynomialOrder2, self).setUp()
-
-
-class TestPolynomialOrder3(CommonTests, unittest.TestCase):
- # class Polynomial constructed with order=3
-
- def setUp(self):
- self.true_values = lambda: dict(c3=2, c2=5, c1=2, c0=8)
- self.guess = lambda: dict(c3=1, c1=1, c2=6, c0=3)
- self.model_constructor = models.PolynomialModel
- self.args = (3,)
- super(TestPolynomialOrder3, self).setUp()
-
-
-class TestConstant(CommonTests, unittest.TestCase):
-
- def setUp(self):
- self.true_values = lambda: dict(c=5)
- self.guess = lambda: dict(c=2)
- self.model_constructor = models.ConstantModel
- super(TestConstant, self).setUp()
-
- def check_skip_independent_vars(self):
- raise nose.SkipTest("ConstantModel has not independent_vars.")
-
-class TestPowerlaw(CommonTests, unittest.TestCase):
-
- def setUp(self):
- self.true_values = lambda: dict(amplitude=5, exponent=3)
- self.guess = lambda: dict(amplitude=2, exponent=8)
- self.model_constructor = models.PowerLawModel
- super(TestPowerlaw, self).setUp()
-
-
-class TestExponential(CommonTests, unittest.TestCase):
-
- def setUp(self):
- self.true_values = lambda: dict(amplitude=5, decay=3)
- self.guess = lambda: dict(amplitude=2, decay=8)
- self.model_constructor = models.ExponentialModel
- super(TestExponential, self).setUp()
+import unittest
+import warnings
+import nose
+from numpy.testing import assert_allclose
+from numpy.testing.decorators import knownfailureif
+import numpy as np
+
+from lmfit import Model, Parameter, models
+from lmfit.lineshapes import gaussian
+
+def assert_results_close(actual, desired, rtol=1e-03, atol=1e-03,
+ err_msg='', verbose=True):
+ for param_name, value in desired.items():
+ assert_allclose(actual[param_name], value, rtol, atol, err_msg, verbose)
+
+def _skip_if_no_pandas():
+ try:
+ import pandas
+ except ImportError:
+ raise nose.SkipTest("Skipping tests that require pandas.")
+
+
+class CommonTests(object):
+ # to be subclassed for testing predefined models
+
+ def setUp(self):
+ np.random.seed(1)
+ self.noise = 0.0001*np.random.randn(*self.x.shape)
+ # Some Models need args (e.g., polynomial order), and others don't.
+ try:
+ args = self.args
+ except AttributeError:
+ self.model = self.model_constructor()
+ self.model_drop = self.model_constructor(missing='drop')
+ self.model_raise = self.model_constructor(missing='raise')
+ self.model_explicit_var = self.model_constructor(['x'])
+ func = self.model.func
+ else:
+ self.model = self.model_constructor(*args)
+ self.model_drop = self.model_constructor(*args, missing='drop')
+ self.model_raise = self.model_constructor(*args, missing='raise')
+ self.model_explicit_var = self.model_constructor(
+ *args, independent_vars=['x'])
+ func = self.model.func
+ self.data = func(x=self.x, **self.true_values()) + self.noise
+
+ @property
+ def x(self):
+ return np.linspace(1, 10, num=1000)
+
+ def test_fit(self):
+ model = self.model
+
+ # Pass Parameters object.
+ params = model.make_params(**self.guess())
+ result = model.fit(self.data, params, x=self.x)
+ assert_results_close(result.values, self.true_values())
+
+ # Pass inidividual Parameter objects as kwargs.
+ kwargs = {name: p for name, p in params.items()}
+ result = self.model.fit(self.data, x=self.x, **kwargs)
+ assert_results_close(result.values, self.true_values())
+
+ # Pass guess values (not Parameter objects) as kwargs.
+ kwargs = {name: p.value for name, p in params.items()}
+ result = self.model.fit(self.data, x=self.x, **kwargs)
+ assert_results_close(result.values, self.true_values())
+
+ def test_explicit_independent_vars(self):
+ self.check_skip_independent_vars()
+ model = self.model_explicit_var
+ pars = model.make_params(**self.guess())
+ result = model.fit(self.data, pars, x=self.x)
+ assert_results_close(result.values, self.true_values())
+
+ def test_fit_with_weights(self):
+ model = self.model
+
+ # fit without weights
+ params = model.make_params(**self.guess())
+ out1 = model.fit(self.data, params, x=self.x)
+
+ # fit with weights
+ weights = 1.0/(0.5 + self.x**2)
+ out2 = model.fit(self.data, params, weights=weights, x=self.x)
+
+ max_diff = 0.0
+ for parname, val1 in out1.values.items():
+ val2 = out2.values[parname]
+ if max_diff < abs(val1-val2):
+ max_diff = abs(val1-val2)
+ assert(max_diff > 1.e-8)
+
+ def test_result_attributes(self):
+ pars = self.model.make_params(**self.guess())
+ result = self.model.fit(self.data, pars, x=self.x)
+
+ # result.init_values
+ assert_results_close(result.values, self.true_values())
+ self.assertEqual(result.init_values, self.guess())
+
+ # result.init_params
+ params = self.model.make_params()
+ for param_name, value in self.guess().items():
+ params[param_name].value = value
+ self.assertEqual(result.init_params, params)
+
+ # result.best_fit
+ assert_allclose(result.best_fit, self.data, atol=self.noise.max())
+
+ # result.init_fit
+ init_fit = self.model.func(x=self.x, **self.guess())
+ assert_allclose(result.init_fit, init_fit)
+
+ # result.model
+ self.assertTrue(result.model is self.model)
+
+ def test_result_eval(self):
+ # Check eval() output against init_fit and best_fit.
+ pars = self.model.make_params(**self.guess())
+ result = self.model.fit(self.data, pars, x=self.x)
+
+ assert_allclose(result.eval(x=self.x, **result.values),
+ result.best_fit)
+ assert_allclose(result.eval(x=self.x, **result.init_values),
+ result.init_fit)
+
+ def test_result_eval_custom_x(self):
+ self.check_skip_independent_vars()
+ pars = self.model.make_params(**self.guess())
+ result = self.model.fit(self.data, pars, x=self.x)
+
+ # Check that the independent variable is respected.
+ short_eval = result.eval(x=np.array([0, 1, 2]), **result.values)
+ self.assertEqual(len(short_eval), 3)
+
+ def test_data_alignment(self):
+ _skip_if_no_pandas()
+ from pandas import Series
+
+ # Align data and indep var of different lengths using pandas index.
+ data = Series(self.data.copy()).iloc[10:-10]
+ x = Series(self.x.copy())
+
+ model = self.model
+ params = model.make_params(**self.guess())
+ result = model.fit(data, params, x=x)
+ result = model.fit(data, params, x=x)
+ assert_results_close(result.values, self.true_values())
+
+ # Skip over missing (NaN) values, aligning via pandas index.
+ data.iloc[500:510] = np.nan
+ result = self.model_drop.fit(data, params, x=x)
+ assert_results_close(result.values, self.true_values())
+
+ # Raise if any NaN values are present.
+ raises = lambda: self.model_raise.fit(data, params, x=x)
+ self.assertRaises(ValueError, raises)
+
+ def check_skip_independent_vars(self):
+ # to be overridden for models that do not accept indep vars
+ pass
+
+ def test_aic(self):
+ model = self.model
+
+ # Pass Parameters object.
+ params = model.make_params(**self.guess())
+ result = model.fit(self.data, params, x=self.x)
+ aic = result.aic
+ self.assertTrue(aic < 0) # aic must be negative
+
+ # Pass extra unused Parameter.
+ params.add("unused_param", value=1.0, vary=True)
+ result = model.fit(self.data, params, x=self.x)
+ aic_extra = result.aic
+ self.assertTrue(aic_extra < 0) # aic must be negative
+ self.assertTrue(aic < aic_extra) # the extra param should lower the aic
+
+
+ def test_bic(self):
+ model = self.model
+
+ # Pass Parameters object.
+ params = model.make_params(**self.guess())
+ result = model.fit(self.data, params, x=self.x)
+ bic = result.bic
+ self.assertTrue(bic < 0) # aic must be negative
+
+ # Compare to AIC
+ aic = result.aic
+ self.assertTrue(aic < bic) # aic should be lower than bic
+
+ # Pass extra unused Parameter.
+ params.add("unused_param", value=1.0, vary=True)
+ result = model.fit(self.data, params, x=self.x)
+ bic_extra = result.bic
+ self.assertTrue(bic_extra < 0) # bic must be negative
+ self.assertTrue(bic < bic_extra) # the extra param should lower the bic
+
+
+class TestUserDefiniedModel(CommonTests, unittest.TestCase):
+ # mainly aimed at checking that the API does what it says it does
+ # and raises the right exceptions or warnings when things are not right
+
+ def setUp(self):
+ self.true_values = lambda: dict(amplitude=7.1, center=1.1, sigma=2.40)
+ self.guess = lambda: dict(amplitude=5, center=2, sigma=4)
+ # return a fresh copy
+ self.model_constructor = (
+ lambda *args, **kwargs: Model(gaussian, *args, **kwargs))
+ super(TestUserDefiniedModel, self).setUp()
+
+ @property
+ def x(self):
+ return np.linspace(-10, 10, num=1000)
+
+ def test_lists_become_arrays(self):
+ # smoke test
+ self.model.fit([1, 2, 3], x=[1, 2, 3], **self.guess())
+ self.model.fit([1, 2, None, 3], x=[1, 2, 3, 4], **self.guess())
+
+ def test_missing_param_raises_error(self):
+
+ # using keyword argument parameters
+ guess_missing_sigma = self.guess()
+ del guess_missing_sigma['sigma']
+ # f = lambda: self.model.fit(self.data, x=self.x, **guess_missing_sigma)
+ # self.assertRaises(ValueError, f)
+
+ # using Parameters
+ params = self.model.make_params()
+ for param_name, value in guess_missing_sigma.items():
+ params[param_name].value = value
+ f = lambda: self.model.fit(self.data, params, x=self.x)
+
+ def test_extra_param_issues_warning(self):
+ # The function accepts extra params, Model will warn but not raise.
+ def flexible_func(x, amplitude, center, sigma, **kwargs):
+ return gaussian(x, amplitude, center, sigma)
+
+ flexible_model = Model(flexible_func)
+ pars = flexible_model.make_params(**self.guess())
+ with warnings.catch_warnings(record=True) as w:
+ warnings.simplefilter("always")
+ flexible_model.fit(self.data, pars, x=self.x, extra=5)
+ self.assertTrue(len(w) == 1)
+ self.assertTrue(issubclass(w[-1].category, UserWarning))
+
+ def test_missing_independent_variable_raises_error(self):
+ pars = self.model.make_params(**self.guess())
+ f = lambda: self.model.fit(self.data, pars)
+ self.assertRaises(KeyError, f)
+
+ def test_bounding(self):
+ true_values = self.true_values()
+ true_values['center'] = 1.3 # as close as it's allowed to get
+ pars = self.model.make_params(**self.guess())
+ pars['center'].set(value=2, min=1.3)
+ result = self.model.fit(self.data, pars, x=self.x)
+ assert_results_close(result.values, true_values, rtol=0.05)
+
+ def test_vary_false(self):
+ true_values = self.true_values()
+ true_values['center'] = 1.3
+ pars = self.model.make_params(**self.guess())
+ pars['center'].set(value=1.3, vary=False)
+ result = self.model.fit(self.data, pars, x=self.x)
+ assert_results_close(result.values, true_values, rtol=0.05)
+
+ # testing model addition...
+
+ def test_user_defined_gaussian_plus_constant(self):
+ data = self.data + 5.0
+ model = self.model + models.ConstantModel()
+ guess = self.guess()
+ pars = model.make_params(c= 10.1, **guess)
+ true_values = self.true_values()
+ true_values['c'] = 5.0
+
+ result = model.fit(data, pars, x=self.x)
+ assert_results_close(result.values, true_values, rtol=0.01, atol=0.01)
+
+ def test_model_with_prefix(self):
+ # model with prefix of 'a' and 'b'
+ mod = models.GaussianModel(prefix='a')
+ vals = {'center': 2.45, 'sigma':0.8, 'amplitude':3.15}
+ data = gaussian(x=self.x, **vals) + self.noise/3.0
+ pars = mod.guess(data, x=self.x)
+ self.assertTrue('aamplitude' in pars)
+ self.assertTrue('asigma' in pars)
+ out = mod.fit(data, pars, x=self.x)
+ self.assertTrue(out.params['aamplitude'].value > 2.0)
+ self.assertTrue(out.params['acenter'].value > 2.0)
+ self.assertTrue(out.params['acenter'].value < 3.0)
+
+ mod = models.GaussianModel(prefix='b')
+ data = gaussian(x=self.x, **vals) + self.noise/3.0
+ pars = mod.guess(data, x=self.x)
+ self.assertTrue('bamplitude' in pars)
+ self.assertTrue('bsigma' in pars)
+
+ def test_change_prefix(self):
+ "should fail"
+ mod = models.GaussianModel(prefix='b')
+ set_prefix_failed = None
+ try:
+ mod.prefix = 'c'
+ set_prefix_failed = False
+ except AttributeError:
+ set_prefix_failed = True
+ except:
+ set_prefix_failed = None
+ self.assertTrue(set_prefix_failed)
+
+
+ def test_sum_of_two_gaussians(self):
+ # two user-defined gaussians
+ model1 = self.model
+ f2 = lambda x, amp, cen, sig: gaussian(x, amplitude=amp, center=cen, sigma=sig)
+ model2 = Model(f2)
+ values1 = self.true_values()
+ values2 = {'cen': 2.45, 'sig':0.8, 'amp':3.15}
+
+ data = gaussian(x=self.x, **values1) + f2(x=self.x, **values2) + self.noise/3.0
+ model = self.model + model2
+ pars = model.make_params()
+ pars['sigma'].set(value=2, min=0)
+ pars['center'].set(value=1, min=0.2, max=1.8)
+ pars['amplitude'].set(value=3, min=0)
+ pars['sig'].set(value=1, min=0)
+ pars['cen'].set(value=2.4, min=2, max=3.5)
+ pars['amp'].set(value=1, min=0)
+
+ true_values = dict(list(values1.items()) + list(values2.items()))
+ result = model.fit(data, pars, x=self.x)
+ assert_results_close(result.values, true_values, rtol=0.01, atol=0.01)
+
+ # user-defined models with common parameter names
+ # cannot be added, and should raise
+ f = lambda: model1 + model1
+ self.assertRaises(NameError, f)
+
+ # two predefined_gaussians, using suffix to differentiate
+ model1 = models.GaussianModel(prefix='g1_')
+ model2 = models.GaussianModel(prefix='g2_')
+ model = model1 + model2
+ true_values = {'g1_center': values1['center'],
+ 'g1_amplitude': values1['amplitude'],
+ 'g1_sigma': values1['sigma'],
+ 'g2_center': values2['cen'],
+ 'g2_amplitude': values2['amp'],
+ 'g2_sigma': values2['sig']}
+ pars = model.make_params()
+ pars['g1_sigma'].set(2)
+ pars['g1_center'].set(1)
+ pars['g1_amplitude'].set(3)
+ pars['g2_sigma'].set(1)
+ pars['g2_center'].set(2.4)
+ pars['g2_amplitude'].set(1)
+
+ result = model.fit(data, pars, x=self.x)
+ assert_results_close(result.values, true_values, rtol=0.01, atol=0.01)
+
+ # without suffix, the names collide and Model should raise
+ model1 = models.GaussianModel()
+ model2 = models.GaussianModel()
+ f = lambda: model1 + model2
+ self.assertRaises(NameError, f)
+
+ def test_sum_composite_models(self):
+ # test components of composite model created adding composite model
+ model1 = models.GaussianModel(prefix='g1_')
+ model2 = models.GaussianModel(prefix='g2_')
+ model3 = models.GaussianModel(prefix='g3_')
+ model4 = models.GaussianModel(prefix='g4_')
+
+ model_total1 = (model1 + model2) + model3
+ for mod in [model1, model2, model3]:
+ self.assertTrue(mod in model_total1.components)
+
+ model_total2 = model1 + (model2 + model3)
+ for mod in [model1, model2, model3]:
+ self.assertTrue(mod in model_total2.components)
+
+ model_total3 = (model1 + model2) + (model3 + model4)
+ for mod in [model1, model2, model3, model4]:
+ self.assertTrue(mod in model_total3.components)
+
+ def test_composite_has_bestvalues(self):
+ # test that a composite model has non-empty best_values
+ model1 = models.GaussianModel(prefix='g1_')
+ model2 = models.GaussianModel(prefix='g2_')
+
+ mod = model1 + model2
+ pars = mod.make_params()
+
+ values1 = dict(amplitude=7.10, center=1.1, sigma=2.40)
+ values2 = dict(amplitude=12.2, center=2.5, sigma=0.5)
+ data = gaussian(x=self.x, **values1) + gaussian(x=self.x, **values2) + 0.1*self.noise
+
+ pars['g1_sigma'].set(2)
+ pars['g1_center'].set(1, max=1.5)
+ pars['g1_amplitude'].set(3)
+ pars['g2_sigma'].set(1)
+ pars['g2_center'].set(2.6, min=2.0)
+ pars['g2_amplitude'].set(1)
+
+ result = mod.fit(data, params=pars, x=self.x)
+
+ self.assertTrue(len(result.best_values) == 6)
+
+ self.assertTrue(abs(result.params['g1_amplitude'].value - 7.1) < 0.5)
+ self.assertTrue(abs(result.params['g2_amplitude'].value - 12.2) < 0.5)
+ self.assertTrue(abs(result.params['g1_center'].value - 1.1) < 0.2)
+ self.assertTrue(abs(result.params['g2_center'].value - 2.5) < 0.2)
+
+
+ def test_hints_in_composite_models(self):
+ # test propagation of hints from base models to composite model
+ def func(x, amplitude):
+ pass
+
+ m1 = Model(func, prefix='p1_')
+ m2 = Model(func, prefix='p2_')
+
+ m1.set_param_hint('amplitude', value=1)
+ m2.set_param_hint('amplitude', value=2)
+
+ mx = (m1 + m2)
+ params = mx.make_params()
+ param_values = {name: p.value for name, p in params.items()}
+ self.assertEqual(param_values['p1_amplitude'], 1)
+ self.assertEqual(param_values['p2_amplitude'], 2)
+
+ def test_hints_for_peakmodels(self):
+ # test that height/fwhm do not cause asteval errors.
+
+ x = np.linspace(-10, 10, 101)
+ y = np.sin(x / 3) + x /100.
+
+ m1 = models.LinearModel(prefix='m1_')
+
+ params = m1.guess(y, x=x)
+
+ m2 = models.GaussianModel(prefix='m2_')
+ params.update(m2.make_params())
+
+ m = m1 + m2
+
+ param_values = {name: p.value for name, p in params.items()}
+ self.assertTrue(param_values['m1_intercept'] < -0.0)
+ self.assertEqual(param_values['m2_amplitude'], 1)
+
+ def test_weird_param_hints(self):
+ # tests Github Issue 312, a very weird way to access param_hints
+ def func(x, amp):
+ return amp*x
+
+ m = Model(func)
+ models = {}
+ for i in range(2):
+ m.set_param_hint('amp', value=1)
+ m.set_param_hint('amp', value=25)
+
+ models[i] = Model(func, prefix='mod%i_' % i)
+ models[i].param_hints['amp'] = m.param_hints['amp']
+
+ self.assertEqual(models[0].param_hints['amp'],
+ models[1].param_hints['amp'])
+
+
+ def test_composite_model_with_expr_constrains(self):
+ """Smoke test for composite model fitting with expr constraints.
+ """
+ y = [ 0, 0, 4, 2, 1, 8, 21, 21, 23, 35, 50, 54, 46,
+ 70, 77, 87, 98, 113, 148, 136, 185, 195, 194, 168, 170, 139,
+ 155, 115, 132, 109, 102, 85, 69, 81, 82, 80, 71, 64, 79,
+ 88, 111, 97, 97, 73, 72, 62, 41, 30, 13, 3, 9, 7,
+ 0, 0, 0]
+ x = np.arange(-0.2, 1.2, 0.025)[:-1] + 0.5*0.025
+
+ def gauss(x, sigma, mu, A):
+ return A*np.exp(-(x-mu)**2/(2*sigma**2))
+
+ # Initial values
+ p1_mu = 0.2
+ p1_sigma = 0.1
+ #p2_mu = 0.8
+ p2_sigma = 0.1
+
+ peak1 = Model(gauss, prefix='p1_')
+ peak2 = Model(gauss, prefix='p2_')
+ model = peak1 + peak2
+
+ model.set_param_hint('p1_mu', value=p1_mu, min=-1, max=2)
+ #model.set_param_hint('p2_mu', value=p2_mu, min=-1, max=2)
+ model.set_param_hint('p1_sigma', value=p1_sigma, min=0.01, max=0.2)
+ model.set_param_hint('p2_sigma', value=p2_sigma, min=0.01, max=0.2)
+ model.set_param_hint('p1_A', value=100, min=0.01)
+ model.set_param_hint('p2_A', value=50, min=0.01)
+
+ # Constrains the distance between peaks to be > 0
+ model.set_param_hint('pos_delta', value=0.3, min=0)
+ model.set_param_hint('p2_mu', min=-1, expr='p1_mu + pos_delta')
+
+ # Test fitting
+ result = model.fit(y, x=x)
+ self.assertTrue(result.params['pos_delta'].value > 0)
+
+
+class TestLinear(CommonTests, unittest.TestCase):
+
+ def setUp(self):
+ self.true_values = lambda: dict(slope=5, intercept=2)
+ self.guess = lambda: dict(slope=10, intercept=6)
+ self.model_constructor = models.LinearModel
+ super(TestLinear, self).setUp()
+
+
+class TestParabolic(CommonTests, unittest.TestCase):
+
+ def setUp(self):
+ self.true_values = lambda: dict(a=5, b=2, c=8)
+ self.guess = lambda: dict(a=1, b=6, c=3)
+ self.model_constructor = models.ParabolicModel
+ super(TestParabolic, self).setUp()
+
+
+class TestPolynomialOrder2(CommonTests, unittest.TestCase):
+ # class Polynomial constructed with order=2
+
+ def setUp(self):
+ self.true_values = lambda: dict(c2=5, c1=2, c0=8)
+ self.guess = lambda: dict(c1=1, c2=6, c0=3)
+ self.model_constructor = models.PolynomialModel
+ self.args = (2,)
+ super(TestPolynomialOrder2, self).setUp()
+
+
+class TestPolynomialOrder3(CommonTests, unittest.TestCase):
+ # class Polynomial constructed with order=3
+
+ def setUp(self):
+ self.true_values = lambda: dict(c3=2, c2=5, c1=2, c0=8)
+ self.guess = lambda: dict(c3=1, c1=1, c2=6, c0=3)
+ self.model_constructor = models.PolynomialModel
+ self.args = (3,)
+ super(TestPolynomialOrder3, self).setUp()
+
+
+class TestConstant(CommonTests, unittest.TestCase):
+ def setUp(self):
+ self.true_values = lambda: dict(c=5)
+ self.guess = lambda: dict(c=2)
+ self.model_constructor = models.ConstantModel
+ super(TestConstant, self).setUp()
+
+ def check_skip_independent_vars(self):
+ raise nose.SkipTest("ConstantModel has not independent_vars.")
+
+class TestPowerlaw(CommonTests, unittest.TestCase):
+ def setUp(self):
+ self.true_values = lambda: dict(amplitude=5, exponent=3)
+ self.guess = lambda: dict(amplitude=2, exponent=8)
+ self.model_constructor = models.PowerLawModel
+ super(TestPowerlaw, self).setUp()
+
+
+class TestExponential(CommonTests, unittest.TestCase):
+ def setUp(self):
+ self.true_values = lambda: dict(amplitude=5, decay=3)
+ self.guess = lambda: dict(amplitude=2, decay=8)
+ self.model_constructor = models.ExponentialModel
+ super(TestExponential, self).setUp()
+
+
+class TestComplexConstant(CommonTests, unittest.TestCase):
+ def setUp(self):
+ self.true_values = lambda: dict(re=5,im=5)
+ self.guess = lambda: dict(re=2,im=2)
+ self.model_constructor = models.ComplexConstantModel
+ super(TestComplexConstant, self).setUp()
+
+#
diff --git a/tests/test_multidatasets.py b/tests/test_multidatasets.py
index 105a8cf..985a70c 100644
--- a/tests/test_multidatasets.py
+++ b/tests/test_multidatasets.py
@@ -1,74 +1,74 @@
-#
-# example fitting to multiple (simulated) data sets
-#
-import numpy as np
-from lmfit import minimize, Parameters, fit_report
-from lmfit.lineshapes import gaussian
-
-def gauss_dataset(params, i, x):
- """calc gaussian from params for data set i
- using simple, hardwired naming convention"""
- amp = params['amp_%i' % (i+1)].value
- cen = params['cen_%i' % (i+1)].value
- sig = params['sig_%i' % (i+1)].value
- return gaussian(x, amp, cen, sig)
-
-def objective(params, x, data):
- """ calculate total residual for fits to several data sets held
- in a 2-D array, and modeled by Gaussian functions"""
- ndata, nx = data.shape
- resid = 0.0*data[:]
- # make residual per data set
- for i in range(ndata):
- resid[i, :] = data[i, :] - gauss_dataset(params, i, x)
- # now flatten this to a 1D array, as minimize() needs
- return resid.flatten()
-
-def test_multidatasets():
- # create 5 datasets
- x = np.linspace( -1, 2, 151)
- data = []
- for i in np.arange(5):
- amp = 2.60 + 1.50*np.random.rand()
- cen = -0.20 + 1.50*np.random.rand()
- sig = 0.25 + 0.03*np.random.rand()
- dat = gaussian(x, amp, cen, sig) + \
- np.random.normal(size=len(x), scale=0.1)
- data.append(dat)
-
- # data has shape (5, 151)
- data = np.array(data)
- assert(data.shape) == (5, 151)
-
- # create 5 sets of parameters, one per data set
- pars = Parameters()
- for iy, y in enumerate(data):
- pars.add( 'amp_%i' % (iy+1), value=0.5, min=0.0, max=200)
- pars.add( 'cen_%i' % (iy+1), value=0.4, min=-2.0, max=2.0)
- pars.add( 'sig_%i' % (iy+1), value=0.3, min=0.01, max=3.0)
-
- # but now constrain all values of sigma to have the same value
- # by assigning sig_2, sig_3, .. sig_5 to be equal to sig_1
- for iy in (2, 3, 4, 5):
- pars['sig_%i' % iy].expr='sig_1'
-
- # run the global fit to all the data sets
- out = minimize(objective, pars, args=(x, data))
-
- assert(len(pars) == 15)
- assert(out.nvarys == 11)
- assert(out.nfev > 15)
- assert(out.chisqr > 1.0)
- assert(pars['amp_1'].value > 0.1)
- assert(pars['sig_1'].value > 0.1)
- assert(pars['sig_2'].value == pars['sig_1'].value)
-
- ## plot the data sets and fits
- # plt.figure()
- # for i in range(5):
- # y_fit = gauss_dataset(pars, i, x)
- # plt.plot(x, data[i, :], 'o', x, y_fit, '-')
- # plt.show()
-
-if __name__ == '__main__':
- test_multidatasets()
+#
+# example fitting to multiple (simulated) data sets
+#
+import numpy as np
+from lmfit import minimize, Parameters, fit_report
+from lmfit.lineshapes import gaussian
+
+def gauss_dataset(params, i, x):
+ """calc gaussian from params for data set i
+ using simple, hardwired naming convention"""
+ amp = params['amp_%i' % (i+1)].value
+ cen = params['cen_%i' % (i+1)].value
+ sig = params['sig_%i' % (i+1)].value
+ return gaussian(x, amp, cen, sig)
+
+def objective(params, x, data):
+ """ calculate total residual for fits to several data sets held
+ in a 2-D array, and modeled by Gaussian functions"""
+ ndata, nx = data.shape
+ resid = 0.0*data[:]
+ # make residual per data set
+ for i in range(ndata):
+ resid[i, :] = data[i, :] - gauss_dataset(params, i, x)
+ # now flatten this to a 1D array, as minimize() needs
+ return resid.flatten()
+
+def test_multidatasets():
+ # create 5 datasets
+ x = np.linspace( -1, 2, 151)
+ data = []
+ for i in np.arange(5):
+ amp = 2.60 + 1.50*np.random.rand()
+ cen = -0.20 + 1.50*np.random.rand()
+ sig = 0.25 + 0.03*np.random.rand()
+ dat = gaussian(x, amp, cen, sig) + \
+ np.random.normal(size=len(x), scale=0.1)
+ data.append(dat)
+
+ # data has shape (5, 151)
+ data = np.array(data)
+ assert(data.shape) == (5, 151)
+
+ # create 5 sets of parameters, one per data set
+ pars = Parameters()
+ for iy, y in enumerate(data):
+ pars.add( 'amp_%i' % (iy+1), value=0.5, min=0.0, max=200)
+ pars.add( 'cen_%i' % (iy+1), value=0.4, min=-2.0, max=2.0)
+ pars.add( 'sig_%i' % (iy+1), value=0.3, min=0.01, max=3.0)
+
+ # but now constrain all values of sigma to have the same value
+ # by assigning sig_2, sig_3, .. sig_5 to be equal to sig_1
+ for iy in (2, 3, 4, 5):
+ pars['sig_%i' % iy].expr='sig_1'
+
+ # run the global fit to all the data sets
+ out = minimize(objective, pars, args=(x, data))
+
+ assert(len(pars) == 15)
+ assert(out.nvarys == 11)
+ assert(out.nfev > 15)
+ assert(out.chisqr > 1.0)
+ assert(pars['amp_1'].value > 0.1)
+ assert(pars['sig_1'].value > 0.1)
+ assert(pars['sig_2'].value == pars['sig_1'].value)
+
+ ## plot the data sets and fits
+ # plt.figure()
+ # for i in range(5):
+ # y_fit = gauss_dataset(pars, i, x)
+ # plt.plot(x, data[i, :], 'o', x, y_fit, '-')
+ # plt.show()
+
+if __name__ == '__main__':
+ test_multidatasets()
diff --git a/tests/test_nose.py b/tests/test_nose.py
index 3d0095f..b5ad44a 100644
--- a/tests/test_nose.py
+++ b/tests/test_nose.py
@@ -1,399 +1,608 @@
-# -*- coding: utf-8 -*-
-from __future__ import print_function
-from lmfit import minimize, Parameters, Parameter, report_fit, Minimizer
-from lmfit.minimizer import SCALAR_METHODS
-from lmfit.lineshapes import gaussian
-import numpy as np
-from numpy import pi
-from numpy.testing import assert_
-import unittest
-import nose
-from nose import SkipTest
-
-def check(para, real_val, sig=3):
- err = abs(para.value - real_val)
- print( para.name, para.value, real_val, para.stderr)
- assert(err < sig * para.stderr)
-
-def check_wo_stderr(para, real_val, sig=0.1):
- err = abs(para.value - real_val)
- print (para.name, para.value, real_val)
- assert(err < sig)
-
-def check_paras(para_fit, para_real):
- for i in para_fit:
- check(para_fit[i], para_real[i].value)
-
-def test_simple():
- # create data to be fitted
- np.random.seed(1)
- x = np.linspace(0, 15, 301)
- data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) +
- np.random.normal(size=len(x), scale=0.2) )
-
- # define objective function: returns the array to be minimized
- def fcn2min(params, x, data):
- """ model decaying sine wave, subtract data"""
- amp = params['amp'].value
- shift = params['shift'].value
- omega = params['omega'].value
- decay = params['decay'].value
-
- model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay)
- return model - data
-
- # create a set of Parameters
- params = Parameters()
- params.add('amp', value= 10, min=0)
- params.add('decay', value= 0.1)
- params.add('shift', value= 0.0, min=-pi / 2., max=pi / 2)
- params.add('omega', value= 3.0)
-
- # do fit, here with leastsq model
- result = minimize(fcn2min, params, args=(x, data))
-
- # calculate final result
- final = data + result.residual
-
- # write error report
- print(" --> SIMPLE --> ")
- print(result.params)
- report_fit(result.params)
-
- #assert that the real parameters are found
-
- for para, val in zip(result.params.values(), [5, 0.025, -.1, 2]):
-
- check(para, val)
-
-def test_lbfgsb():
- p_true = Parameters()
- p_true.add('amp', value=14.0)
- p_true.add('period', value=5.33)
- p_true.add('shift', value=0.123)
- p_true.add('decay', value=0.010)
-
- def residual(pars, x, data=None):
- amp = pars['amp'].value
- per = pars['period'].value
- shift = pars['shift'].value
- decay = pars['decay'].value
-
- if abs(shift) > pi/2:
- shift = shift - np.sign(shift) * pi
- model = amp * np.sin(shift + x / per) * np.exp(-x * x * decay * decay)
- if data is None:
- return model
- return (model - data)
-
- n = 2500
- xmin = 0.
- xmax = 250.0
- noise = np.random.normal(scale=0.7215, size=n)
- x = np.linspace(xmin, xmax, n)
- data = residual(p_true, x) + noise
-
- fit_params = Parameters()
- fit_params.add('amp', value=11.0, min=5, max=20)
- fit_params.add('period', value=5., min=1., max=7)
- fit_params.add('shift', value=.10, min=0.0, max=0.2)
- fit_params.add('decay', value=6.e-3, min=0, max=0.1)
-
- init = residual(fit_params, x)
-
- out = minimize(residual, fit_params, method='lbfgsb', args=(x,), kws={'data':data})
-
- fit = residual(fit_params, x)
-
- for name, par in out.params.items():
- nout = "%s:%s" % (name, ' '*(20-len(name)))
- print("%s: %s (%s) " % (nout, par.value, p_true[name].value))
-
- for para, true_para in zip(out.params.values(), p_true.values()):
- check_wo_stderr(para, true_para.value)
-
-def test_derive():
- def func(pars, x, data=None):
- a = pars['a'].value
- b = pars['b'].value
- c = pars['c'].value
-
- model=a * np.exp(-b * x)+c
- if data is None:
- return model
- return (model - data)
-
- def dfunc(pars, x, data=None):
- a = pars['a'].value
- b = pars['b'].value
- c = pars['c'].value
- v = np.exp(-b*x)
- return np.array([v, -a*x*v, np.ones(len(x))])
-
- def f(var, x):
- return var[0]* np.exp(-var[1] * x)+var[2]
-
- params1 = Parameters()
- params1.add('a', value=10)
- params1.add('b', value=10)
- params1.add('c', value=10)
-
- params2 = Parameters()
- params2.add('a', value=10)
- params2.add('b', value=10)
- params2.add('c', value=10)
-
- a, b, c = 2.5, 1.3, 0.8
- x = np.linspace(0,4,50)
- y = f([a, b, c], x)
- data = y + 0.15*np.random.normal(size=len(x))
-
- # fit without analytic derivative
- min1 = Minimizer(func, params1, fcn_args=(x,), fcn_kws={'data':data})
- out1 = min1.leastsq()
- fit1 = func(out1.params, x)
-
- # fit with analytic derivative
- min2 = Minimizer(func, params2, fcn_args=(x,), fcn_kws={'data':data})
- out2 = min2.leastsq(Dfun=dfunc, col_deriv=1)
- fit2 = func(out2.params, x)
-
-
- print ('''Comparison of fit to exponential decay
- with and without analytic derivatives, to
- model = a*exp(-b*x) + c
- for a = %.2f, b = %.2f, c = %.2f
- ==============================================
- Statistic/Parameter| Without | With |
- ----------------------------------------------
- N Function Calls | %3i | %3i |
- Chi-square | %.4f | %.4f |
- a | %.4f | %.4f |
- b | %.4f | %.4f |
- c | %.4f | %.4f |
- ----------------------------------------------
- ''' % (a, b, c,
- out1.nfev, out2.nfev,
- out1.chisqr, out2.chisqr,
- out1.params['a'].value, out2.params['a'].value,
- out1.params['b'].value, out2.params['b'].value,
- out1.params['c'].value, out2.params['c'].value ))
-
- check_wo_stderr(out1.params['a'], out2.params['a'].value, 0.00005)
- check_wo_stderr(out1.params['b'], out2.params['b'].value, 0.00005)
- check_wo_stderr(out1.params['c'], out2.params['c'].value, 0.00005)
-
-def test_peakfit():
- def residual(pars, x, data=None):
- g1 = gaussian(x, pars['a1'].value, pars['c1'].value, pars['w1'].value)
- g2 = gaussian(x, pars['a2'].value, pars['c2'].value, pars['w2'].value)
- model = g1 + g2
- if data is None:
- return model
- return (model - data)
-
- n = 601
- xmin = 0.
- xmax = 15.0
- noise = np.random.normal(scale=.65, size=n)
- x = np.linspace(xmin, xmax, n)
-
- org_params = Parameters()
- org_params.add_many(('a1', 12.0, True, None, None, None),
- ('c1', 5.3, True, None, None, None),
- ('w1', 1.0, True, None, None, None),
- ('a2', 9.1, True, None, None, None),
- ('c2', 8.1, True, None, None, None),
- ('w2', 2.5, True, None, None, None))
-
- data = residual(org_params, x) + noise
-
-
- fit_params = Parameters()
- fit_params.add_many(('a1', 8.0, True, None, 14., None),
- ('c1', 5.0, True, None, None, None),
- ('w1', 0.7, True, None, None, None),
- ('a2', 3.1, True, None, None, None),
- ('c2', 8.8, True, None, None, None))
-
- fit_params.add('w2', expr='2.5*w1')
-
- myfit = Minimizer(residual, fit_params,
- fcn_args=(x,), fcn_kws={'data':data})
-
- myfit.prepare_fit()
-
- init = residual(fit_params, x)
-
-
- out = myfit.leastsq()
-
- # print(' N fev = ', myfit.nfev)
- # print(myfit.chisqr, myfit.redchi, myfit.nfree)
-
- report_fit(out.params)
-
- fit = residual(out.params, x)
- check_paras(out.params, org_params)
-
-
-def test_scalar_minimize_has_no_uncertainties():
- # scalar_minimize doesn't calculate uncertainties.
- # when a scalar_minimize is run the stderr and correl for each parameter
- # should be None. (stderr and correl are set to None when a Parameter is
- # initialised).
- # This requires a reset after a leastsq fit has been done.
- # Only when scalar_minimize calculates stderr and correl can this test
- # be removed.
-
- np.random.seed(1)
- x = np.linspace(0, 15, 301)
- data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) +
- np.random.normal(size=len(x), scale=0.2) )
-
- # define objective function: returns the array to be minimized
- def fcn2min(params, x, data):
- """ model decaying sine wave, subtract data"""
- amp = params['amp'].value
- shift = params['shift'].value
- omega = params['omega'].value
- decay = params['decay'].value
-
- model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay)
- return model - data
-
- # create a set of Parameters
- params = Parameters()
- params.add('amp', value= 10, min=0)
- params.add('decay', value= 0.1)
- params.add('shift', value= 0.0, min=-pi / 2., max=pi / 2)
- params.add('omega', value= 3.0)
-
- mini = Minimizer(fcn2min, params, fcn_args=(x, data))
- out = mini.minimize()
- assert_(np.isfinite(out.params['amp'].stderr))
- print(out.errorbars)
- assert_(out.errorbars == True)
- out2 = mini.minimize(method='nelder-mead')
- assert_(out2.params['amp'].stderr is None)
- assert_(out2.params['decay'].stderr is None)
- assert_(out2.params['shift'].stderr is None)
- assert_(out2.params['omega'].stderr is None)
- assert_(out2.params['amp'].correl is None)
- assert_(out2.params['decay'].correl is None)
- assert_(out2.params['shift'].correl is None)
- assert_(out2.params['omega'].correl is None)
- assert_(out2.errorbars == False)
-
-
-def test_multidimensional_fit_GH205():
- # test that you don't need to flatten the output from the objective
- # function. Tests regression for GH205.
- pos = np.linspace(0, 99, 100)
- xv, yv = np.meshgrid(pos, pos)
- f = lambda xv, yv, lambda1, lambda2: (np.sin(xv * lambda1)
- + np.cos(yv * lambda2))
-
- data = f(xv, yv, 0.3, 3)
- assert_(data.ndim, 2)
-
- def fcn2min(params, xv, yv, data):
- """ model decaying sine wave, subtract data"""
- lambda1 = params['lambda1'].value
- lambda2 = params['lambda2'].value
- model = f(xv, yv, lambda1, lambda2)
- return model - data
-
- # create a set of Parameters
- params = Parameters()
- params.add('lambda1', value=0.4)
- params.add('lambda2', value=3.2)
-
- mini = Minimizer(fcn2min, params, fcn_args=(xv, yv, data))
- res = mini.minimize()
-
-class CommonMinimizerTest(unittest.TestCase):
-
- def setUp(self):
- """
- test scale minimizers except newton-cg (needs jacobian) and
- anneal (doesn't work out of the box).
- """
- p_true = Parameters()
- p_true.add('amp', value=14.0)
- p_true.add('period', value=5.33)
- p_true.add('shift', value=0.123)
- p_true.add('decay', value=0.010)
- self.p_true = p_true
-
- n = 2500
- xmin = 0.
- xmax = 250.0
- noise = np.random.normal(scale=0.7215, size=n)
- self.x = np.linspace(xmin, xmax, n)
- data = self.residual(p_true, self.x) + noise
-
- fit_params = Parameters()
- fit_params.add('amp', value=11.0, min=5, max=20)
- fit_params.add('period', value=5., min=1., max=7)
- fit_params.add('shift', value=.10, min=0.0, max=0.2)
- fit_params.add('decay', value=6.e-3, min=0, max=0.1)
- self.fit_params = fit_params
-
- init = self.residual(fit_params, self.x)
- self.mini = Minimizer(self.residual, fit_params, [self.x, data])
-
- def residual(self, pars, x, data=None):
- amp = pars['amp'].value
- per = pars['period'].value
- shift = pars['shift'].value
- decay = pars['decay'].value
-
- if abs(shift) > pi/2:
- shift = shift - np.sign(shift) * pi
- model = amp*np.sin(shift + x/per) * np.exp(-x*x*decay*decay)
- if data is None:
- return model
- return (model - data)
-
- def test_diffev_bounds_check(self):
- # You need finite (min, max) for each parameter if you're using
- # differential_evolution.
- self.fit_params['decay'].min = None
- self.minimizer = 'differential_evolution'
- np.testing.assert_raises(ValueError, self.scalar_minimizer)
-
- def test_scalar_minimizers(self):
- # test all the scalar minimizers
- for method in SCALAR_METHODS:
- if method in ['newton', 'dogleg', 'trust-ncg']:
- continue
- self.minimizer = SCALAR_METHODS[method]
- if method == 'Nelder-Mead':
- sig = 0.2
- else:
- sig = 0.15
- self.scalar_minimizer(sig=sig)
-
- def scalar_minimizer(self, sig=0.15):
- try:
- from scipy.optimize import minimize as scipy_minimize
- except ImportError:
- raise SkipTest
-
- print(self.minimizer)
- out = self.mini.scalar_minimize(method=self.minimizer)
-
- fit = self.residual(out.params, self.x)
-
- for name, par in out.params.items():
- nout = "%s:%s" % (name, ' '*(20-len(name)))
- print("%s: %s (%s) " % (nout, par.value, self.p_true[name].value))
-
- for para, true_para in zip(out.params.values(),
- self.p_true.values()):
- check_wo_stderr(para, true_para.value, sig=sig)
-
-
-if __name__ == '__main__':
- nose.main()
+# -*- coding: utf-8 -*-
+from __future__ import print_function
+from lmfit import minimize, Parameters, Parameter, report_fit, Minimizer
+from lmfit.minimizer import (SCALAR_METHODS, HAS_EMCEE,
+ MinimizerResult, _lnpost)
+from lmfit.lineshapes import gaussian
+import numpy as np
+from numpy import pi
+from numpy.testing import (assert_, decorators, assert_raises,
+ assert_almost_equal)
+import unittest
+import nose
+from nose import SkipTest
+
+
+def check(para, real_val, sig=3):
+ err = abs(para.value - real_val)
+ print('Check Param w/ stderr: ', para.name, para.value, real_val, para.stderr)
+ assert(err < sig * para.stderr)
+
+def check_wo_stderr(para, real_val, sig=0.1):
+ err = abs(para.value - real_val)
+ print('Check Param w/o stderr: ', para.name, para.value, real_val, sig)
+ assert(err < sig)
+
+def check_paras(para_fit, para_real, sig=3):
+ for i in para_fit:
+ check(para_fit[i], para_real[i].value, sig=sig)
+
+def test_simple():
+ # create data to be fitted
+ np.random.seed(1)
+ x = np.linspace(0, 15, 301)
+ data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) +
+ np.random.normal(size=len(x), scale=0.2))
+
+ # define objective function: returns the array to be minimized
+ def fcn2min(params, x, data):
+ """ model decaying sine wave, subtract data"""
+ amp = params['amp'].value
+ shift = params['shift'].value
+ omega = params['omega'].value
+ decay = params['decay'].value
+
+ model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay)
+ return model - data
+
+ # create a set of Parameters
+ params = Parameters()
+ params.add('amp', value= 10, min=0)
+ params.add('decay', value= 0.1)
+ params.add('shift', value= 0.0, min=-pi / 2., max=pi / 2)
+ params.add('omega', value= 3.0)
+
+ # do fit, here with leastsq model
+ result = minimize(fcn2min, params, args=(x, data))
+
+ # calculate final result
+ final = data + result.residual
+
+ # write error report
+ print(" --> SIMPLE --> ")
+ print(result.params)
+ report_fit(result.params)
+
+ #assert that the real parameters are found
+
+ for para, val in zip(result.params.values(), [5, 0.025, -.1, 2]):
+
+ check(para, val)
+
+def test_lbfgsb():
+ p_true = Parameters()
+ p_true.add('amp', value=14.0)
+ p_true.add('period', value=5.33)
+ p_true.add('shift', value=0.123)
+ p_true.add('decay', value=0.010)
+
+ def residual(pars, x, data=None):
+ amp = pars['amp'].value
+ per = pars['period'].value
+ shift = pars['shift'].value
+ decay = pars['decay'].value
+
+ if abs(shift) > pi/2:
+ shift = shift - np.sign(shift) * pi
+ model = amp * np.sin(shift + x / per) * np.exp(-x * x * decay * decay)
+ if data is None:
+ return model
+ return (model - data)
+
+ n = 2500
+ xmin = 0.
+ xmax = 250.0
+ noise = np.random.normal(scale=0.7215, size=n)
+ x = np.linspace(xmin, xmax, n)
+ data = residual(p_true, x) + noise
+
+ fit_params = Parameters()
+ fit_params.add('amp', value=11.0, min=5, max=20)
+ fit_params.add('period', value=5., min=1., max=7)
+ fit_params.add('shift', value=.10, min=0.0, max=0.2)
+ fit_params.add('decay', value=6.e-3, min=0, max=0.1)
+
+ init = residual(fit_params, x)
+
+ out = minimize(residual, fit_params, method='lbfgsb', args=(x,), kws={'data':data})
+
+ fit = residual(fit_params, x)
+
+ for name, par in out.params.items():
+ nout = "%s:%s" % (name, ' '*(20-len(name)))
+ print("%s: %s (%s) " % (nout, par.value, p_true[name].value))
+
+ for para, true_para in zip(out.params.values(), p_true.values()):
+ check_wo_stderr(para, true_para.value)
+
+def test_derive():
+ def func(pars, x, data=None):
+ a = pars['a'].value
+ b = pars['b'].value
+ c = pars['c'].value
+
+ model=a * np.exp(-b * x)+c
+ if data is None:
+ return model
+ return model - data
+
+ def dfunc(pars, x, data=None):
+ a = pars['a'].value
+ b = pars['b'].value
+ c = pars['c'].value
+ v = np.exp(-b*x)
+ return np.array([v, -a*x*v, np.ones(len(x))])
+
+ def f(var, x):
+ return var[0]* np.exp(-var[1] * x)+var[2]
+
+ params1 = Parameters()
+ params1.add('a', value=10)
+ params1.add('b', value=10)
+ params1.add('c', value=10)
+
+ params2 = Parameters()
+ params2.add('a', value=10)
+ params2.add('b', value=10)
+ params2.add('c', value=10)
+
+ a, b, c = 2.5, 1.3, 0.8
+ x = np.linspace(0,4,50)
+ y = f([a, b, c], x)
+ data = y + 0.15*np.random.normal(size=len(x))
+
+ # fit without analytic derivative
+ min1 = Minimizer(func, params1, fcn_args=(x,), fcn_kws={'data':data})
+ out1 = min1.leastsq()
+ fit1 = func(out1.params, x)
+
+ # fit with analytic derivative
+ min2 = Minimizer(func, params2, fcn_args=(x,), fcn_kws={'data':data})
+ out2 = min2.leastsq(Dfun=dfunc, col_deriv=1)
+ fit2 = func(out2.params, x)
+
+ print ('''Comparison of fit to exponential decay
+ with and without analytic derivatives, to
+ model = a*exp(-b*x) + c
+ for a = %.2f, b = %.2f, c = %.2f
+ ==============================================
+ Statistic/Parameter| Without | With |
+ ----------------------------------------------
+ N Function Calls | %3i | %3i |
+ Chi-square | %.4f | %.4f |
+ a | %.4f | %.4f |
+ b | %.4f | %.4f |
+ c | %.4f | %.4f |
+ ----------------------------------------------
+ ''' % (a, b, c,
+ out1.nfev, out2.nfev,
+ out1.chisqr, out2.chisqr,
+ out1.params['a'].value, out2.params['a'].value,
+ out1.params['b'].value, out2.params['b'].value,
+ out1.params['c'].value, out2.params['c'].value ))
+
+ check_wo_stderr(out1.params['a'], out2.params['a'].value, 0.00005)
+ check_wo_stderr(out1.params['b'], out2.params['b'].value, 0.00005)
+ check_wo_stderr(out1.params['c'], out2.params['c'].value, 0.00005)
+
+def test_peakfit():
+ def residual(pars, x, data=None):
+ g1 = gaussian(x, pars['a1'].value, pars['c1'].value, pars['w1'].value)
+ g2 = gaussian(x, pars['a2'].value, pars['c2'].value, pars['w2'].value)
+ model = g1 + g2
+ if data is None:
+ return model
+ return (model - data)
+
+ n = 601
+ xmin = 0.
+ xmax = 15.0
+ noise = np.random.normal(scale=.65, size=n)
+ x = np.linspace(xmin, xmax, n)
+
+ org_params = Parameters()
+ org_params.add_many(('a1', 12.0, True, None, None, None),
+ ('c1', 5.3, True, None, None, None),
+ ('w1', 1.0, True, None, None, None),
+ ('a2', 9.1, True, None, None, None),
+ ('c2', 8.1, True, None, None, None),
+ ('w2', 2.5, True, None, None, None))
+
+ data = residual(org_params, x) + noise
+
+
+ fit_params = Parameters()
+ fit_params.add_many(('a1', 8.0, True, None, 14., None),
+ ('c1', 5.0, True, None, None, None),
+ ('w1', 0.7, True, None, None, None),
+ ('a2', 3.1, True, None, None, None),
+ ('c2', 8.8, True, None, None, None))
+
+ fit_params.add('w2', expr='2.5*w1')
+
+ myfit = Minimizer(residual, fit_params,
+ fcn_args=(x,), fcn_kws={'data': data})
+
+ myfit.prepare_fit()
+
+ init = residual(fit_params, x)
+
+
+ out = myfit.leastsq()
+
+ # print(' N fev = ', myfit.nfev)
+ # print(myfit.chisqr, myfit.redchi, myfit.nfree)
+
+ report_fit(out.params)
+
+ fit = residual(out.params, x)
+ check_paras(out.params, org_params)
+
+
+def test_scalar_minimize_has_no_uncertainties():
+ # scalar_minimize doesn't calculate uncertainties.
+ # when a scalar_minimize is run the stderr and correl for each parameter
+ # should be None. (stderr and correl are set to None when a Parameter is
+ # initialised).
+ # This requires a reset after a leastsq fit has been done.
+ # Only when scalar_minimize calculates stderr and correl can this test
+ # be removed.
+
+ np.random.seed(1)
+ x = np.linspace(0, 15, 301)
+ data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) +
+ np.random.normal(size=len(x), scale=0.2) )
+
+ # define objective function: returns the array to be minimized
+ def fcn2min(params, x, data):
+ """ model decaying sine wave, subtract data"""
+ amp = params['amp'].value
+ shift = params['shift'].value
+ omega = params['omega'].value
+ decay = params['decay'].value
+
+ model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay)
+ return model - data
+
+ # create a set of Parameters
+ params = Parameters()
+ params.add('amp', value= 10, min=0)
+ params.add('decay', value= 0.1)
+ params.add('shift', value= 0.0, min=-pi / 2., max=pi / 2)
+ params.add('omega', value= 3.0)
+
+ mini = Minimizer(fcn2min, params, fcn_args=(x, data))
+ out = mini.minimize()
+ assert_(np.isfinite(out.params['amp'].stderr))
+ print(out.errorbars)
+ assert_(out.errorbars == True)
+ out2 = mini.minimize(method='nelder-mead')
+ assert_(out2.params['amp'].stderr is None)
+ assert_(out2.params['decay'].stderr is None)
+ assert_(out2.params['shift'].stderr is None)
+ assert_(out2.params['omega'].stderr is None)
+ assert_(out2.params['amp'].correl is None)
+ assert_(out2.params['decay'].correl is None)
+ assert_(out2.params['shift'].correl is None)
+ assert_(out2.params['omega'].correl is None)
+ assert_(out2.errorbars == False)
+
+
+def test_multidimensional_fit_GH205():
+ # test that you don't need to flatten the output from the objective
+ # function. Tests regression for GH205.
+ pos = np.linspace(0, 99, 100)
+ xv, yv = np.meshgrid(pos, pos)
+ f = lambda xv, yv, lambda1, lambda2: (np.sin(xv * lambda1)
+ + np.cos(yv * lambda2))
+
+ data = f(xv, yv, 0.3, 3)
+ assert_(data.ndim, 2)
+
+ def fcn2min(params, xv, yv, data):
+ """ model decaying sine wave, subtract data"""
+ lambda1 = params['lambda1'].value
+ lambda2 = params['lambda2'].value
+ model = f(xv, yv, lambda1, lambda2)
+ return model - data
+
+ # create a set of Parameters
+ params = Parameters()
+ params.add('lambda1', value=0.4)
+ params.add('lambda2', value=3.2)
+
+ mini = Minimizer(fcn2min, params, fcn_args=(xv, yv, data))
+ res = mini.minimize()
+
+class CommonMinimizerTest(unittest.TestCase):
+
+ def setUp(self):
+ """
+ test scale minimizers except newton-cg (needs jacobian) and
+ anneal (doesn't work out of the box).
+ """
+ p_true = Parameters()
+ p_true.add('amp', value=14.0)
+ p_true.add('period', value=5.33)
+ p_true.add('shift', value=0.123)
+ p_true.add('decay', value=0.010)
+ self.p_true = p_true
+
+ n = 2500
+ xmin = 0.
+ xmax = 250.0
+ noise = np.random.normal(scale=0.7215, size=n)
+ self.x = np.linspace(xmin, xmax, n)
+ self.data = self.residual(p_true, self.x) + noise
+
+ fit_params = Parameters()
+ fit_params.add('amp', value=11.0, min=5, max=20)
+ fit_params.add('period', value=5., min=1., max=7)
+ fit_params.add('shift', value=.10, min=0.0, max=0.2)
+ fit_params.add('decay', value=6.e-3, min=0, max=0.1)
+ self.fit_params = fit_params
+
+ self.mini = Minimizer(self.residual, fit_params, [self.x, self.data])
+
+ def residual(self, pars, x, data=None):
+ amp = pars['amp'].value
+ per = pars['period'].value
+ shift = pars['shift'].value
+ decay = pars['decay'].value
+
+ if abs(shift) > pi/2:
+ shift = shift - np.sign(shift) * pi
+ model = amp*np.sin(shift + x/per) * np.exp(-x*x*decay*decay)
+ if data is None:
+ return model
+ return model - data
+
+ def test_diffev_bounds_check(self):
+ # You need finite (min, max) for each parameter if you're using
+ # differential_evolution.
+ self.fit_params['decay'].min = -np.inf
+ self.minimizer = 'differential_evolution'
+ np.testing.assert_raises(ValueError, self.scalar_minimizer)
+
+ def test_scalar_minimizers(self):
+ # test all the scalar minimizers
+ for method in SCALAR_METHODS:
+ if method in ['newton', 'dogleg', 'trust-ncg', 'cg']:
+ continue
+ self.minimizer = SCALAR_METHODS[method]
+ if method == 'Nelder-Mead':
+ sig = 0.2
+ else:
+ sig = 0.15
+ self.scalar_minimizer(sig=sig)
+
+ def scalar_minimizer(self, sig=0.15):
+ try:
+ from scipy.optimize import minimize as scipy_minimize
+ except ImportError:
+ raise SkipTest
+
+ print(self.minimizer)
+ out = self.mini.scalar_minimize(method=self.minimizer)
+
+ self.residual(out.params, self.x)
+
+ for name, par in out.params.items():
+ nout = "%s:%s" % (name, ' '*(20-len(name)))
+ print("%s: %s (%s) " % (nout, par.value, self.p_true[name].value))
+
+ for para, true_para in zip(out.params.values(),
+ self.p_true.values()):
+ check_wo_stderr(para, true_para.value, sig=sig)
+
+ @decorators.slow
+ def test_emcee(self):
+ # test emcee
+ if not HAS_EMCEE:
+ return True
+
+ np.random.seed(123456)
+ out = self.mini.emcee(nwalkers=100, steps=200,
+ burn=50, thin=10)
+
+ check_paras(out.params, self.p_true, sig=3)
+
+ @decorators.slow
+ def test_emcee_PT(self):
+ # test emcee with parallel tempering
+ if not HAS_EMCEE:
+ return True
+
+ np.random.seed(123456)
+ self.mini.userfcn = residual_for_multiprocessing
+ out = self.mini.emcee(ntemps=4, nwalkers=50, steps=200,
+ burn=100, thin=10, workers=2)
+
+ check_paras(out.params, self.p_true, sig=3)
+
+ @decorators.slow
+ def test_emcee_multiprocessing(self):
+ # test multiprocessing runs
+ if not HAS_EMCEE:
+ return True
+
+ np.random.seed(123456)
+ self.mini.userfcn = residual_for_multiprocessing
+ out = self.mini.emcee(steps=10, workers=4)
+
+ def test_emcee_bounds_length(self):
+ # the log-probability functions check if the parameters are
+ # inside the bounds. Check that the bounds and parameters
+ # are the right lengths for comparison. This can be done
+ # if nvarys != nparams
+ if not HAS_EMCEE:
+ return True
+ self.mini.params['amp'].vary=False
+ self.mini.params['period'].vary=False
+ self.mini.params['shift'].vary=False
+
+ out = self.mini.emcee(steps=10)
+
+ @decorators.slow
+ def test_emcee_partial_bounds(self):
+ # mcmc with partial bounds
+ if not HAS_EMCEE:
+ return True
+
+ np.random.seed(123456)
+ # test mcmc output vs lm, some parameters not bounded
+ self.fit_params['amp'].max = np.inf
+ # self.fit_params['amp'].min = -np.inf
+ out = self.mini.emcee(nwalkers=100, steps=300,
+ burn=100, thin=10)
+
+ check_paras(out.params, self.p_true, sig=3)
+
+ def test_emcee_init_with_chain(self):
+ # can you initialise with a previous chain
+ if not HAS_EMCEE:
+ return True
+
+ out = self.mini.emcee(nwalkers=100, steps=5)
+ # can initialise with a chain
+ out2 = self.mini.emcee(nwalkers=100, steps=1, pos=out.chain)
+
+ # can initialise with a correct subset of a chain
+ out3 = self.mini.emcee(nwalkers=100,
+ steps=1,
+ pos=out.chain[..., -1, :])
+
+ # but you can't initialise if the shape is wrong.
+ assert_raises(ValueError,
+ self.mini.emcee,
+ nwalkers=100,
+ steps=1,
+ pos=out.chain[..., -1, :-1])
+
+ def test_emcee_reuse_sampler(self):
+ if not HAS_EMCEE:
+ return True
+
+ self.mini.emcee(nwalkers=100, steps=5)
+
+ # if you've run the sampler the Minimizer object should have a _lastpos
+ # attribute
+ assert_(hasattr(self.mini, '_lastpos'))
+
+ # now try and re-use sampler
+ out2 = self.mini.emcee(steps=10, reuse_sampler=True)
+ assert_(out2.chain.shape[1] == 15)
+
+ # you shouldn't be able to reuse the sampler if nvarys has changed.
+ self.mini.params['amp'].vary = False
+ assert_raises(ValueError, self.mini.emcee, reuse_sampler=True)
+
+ def test_emcee_lnpost(self):
+ # check ln likelihood is calculated correctly. It should be
+ # -0.5 * chi**2.
+ result = self.mini.minimize()
+
+ # obtain the numeric values
+ # note - in this example all the parameters are varied
+ fvars = np.array([par.value for par in result.params.values()])
+
+ # calculate the cost function with scaled values (parameters all have
+ # lower and upper bounds.
+ scaled_fvars = []
+ for par, fvar in zip(result.params.values(), fvars):
+ par.value = fvar
+ scaled_fvars.append(par.setup_bounds())
+
+ val = self.mini.penalty(np.array(scaled_fvars))
+
+ # calculate the log-likelihood value
+ bounds = np.array([(par.min, par.max)
+ for par in result.params.values()])
+ val2 = _lnpost(fvars,
+ self.residual,
+ result.params,
+ result.var_names,
+ bounds,
+ userargs=(self.x, self.data))
+
+ assert_almost_equal(-0.5 * val, val2)
+
+ def test_emcee_output(self):
+ # test mcmc output
+ if not HAS_EMCEE:
+ return True
+ try:
+ from pandas import DataFrame
+ except ImportError:
+ return True
+ out = self.mini.emcee(nwalkers=10, steps=20, burn=5, thin=2)
+ assert_(isinstance(out, MinimizerResult))
+ assert_(isinstance(out.flatchain, DataFrame))
+
+ # check that we can access the chains via parameter name
+ assert_(out.flatchain['amp'].shape[0] == 80)
+ assert_(out.errorbars is True)
+ assert_(np.isfinite(out.params['amp'].correl['period']))
+
+ # the lnprob array should be the same as the chain size
+ assert_(np.size(out.chain)//4 == np.size(out.lnprob))
+
+ @decorators.slow
+ def test_emcee_float(self):
+ # test that it works if the residuals returns a float, not a vector
+ if not HAS_EMCEE:
+ return True
+
+ def resid(pars, x, data=None):
+ return -0.5 * np.sum(self.residual(pars, x, data=data)**2)
+
+ # just return chi2
+ def resid2(pars, x, data=None):
+ return np.sum(self.residual(pars, x, data=data)**2)
+
+ self.mini.userfcn = resid
+ np.random.seed(123456)
+ out = self.mini.emcee(nwalkers=100, steps=200,
+ burn=50, thin=10)
+ check_paras(out.params, self.p_true, sig=3)
+
+ self.mini.userfcn = resid2
+ np.random.seed(123456)
+ out = self.mini.emcee(nwalkers=100, steps=200,
+ burn=50, thin=10, float_behavior='chi2')
+ check_paras(out.params, self.p_true, sig=3)
+
+ @decorators.slow
+ def test_emcee_seed(self):
+ # test emcee seeding can reproduce a sampling run
+ if not HAS_EMCEE:
+ return True
+
+ out = self.mini.emcee(params=self.fit_params,
+ nwalkers=100,
+ steps=1, seed=1)
+ out2 = self.mini.emcee(params=self.fit_params,
+ nwalkers=100,
+ steps=1, seed=1)
+
+ assert_almost_equal(out.chain, out2.chain)
+
+
+def residual_for_multiprocessing(pars, x, data=None):
+ # a residual function defined in the top level is needed for
+ # multiprocessing. bound methods don't work.
+ amp = pars['amp'].value
+ per = pars['period'].value
+ shift = pars['shift'].value
+ decay = pars['decay'].value
+
+ if abs(shift) > pi/2:
+ shift = shift - np.sign(shift) * pi
+ model = amp*np.sin(shift + x/per) * np.exp(-x*x*decay*decay)
+ if data is None:
+ return model
+ return (model - data)
+
+
+if __name__ == '__main__':
+ nose.main()
diff --git a/tests/test_parameters.py b/tests/test_parameters.py
index beed610..29f3c2d 100644
--- a/tests/test_parameters.py
+++ b/tests/test_parameters.py
@@ -1,107 +1,152 @@
-from __future__ import print_function
-from lmfit import Parameters, Parameter
-from numpy.testing import assert_, assert_almost_equal
-import unittest
-from copy import deepcopy
-import numpy as np
-import pickle
-
-
-class TestParameters(unittest.TestCase):
-
- def setUp(self):
- self.params = Parameters()
- self.params.add_many(('a', 1., True, None, None, None),
- ('b', 2., True, None, None, None),
- ('c', 3., True, None, None, '2. * a'))
-
- def test_expr_was_evaluated(self):
- self.params.update_constraints()
- assert_almost_equal(self.params['c'].value,
- 2 * self.params['a'].value)
-
- def test_deepcopy(self):
- # check that a simple copy works
- b = deepcopy(self.params)
- assert_(self.params == b)
-
- # check that we can add a symbol to the interpreter
- self.params['b'].expr = 'sin(1)'
- self.params['b'].value = 10
- assert_almost_equal(self.params['b'].value, np.sin(1))
- assert_almost_equal(self.params._asteval.symtable['b'], np.sin(1))
-
- # check that the symbols in the interpreter are still the same after
- # deepcopying
- b = deepcopy(self.params)
-
- unique_symbols_params = self.params._asteval.user_defined_symbols()
- unique_symbols_b = self.params._asteval.user_defined_symbols()
- assert_(unique_symbols_b == unique_symbols_params)
- for unique_symbol in unique_symbols_b:
- if self.params._asteval.symtable[unique_symbol] is np.nan:
- continue
-
- assert_(self.params._asteval.symtable[unique_symbol]
- ==
- b._asteval.symtable[unique_symbol])
-
- def test_add_many_params(self):
- # test that we can add many parameters, but only parameters are added.
- a = Parameter('a', 1)
- b = Parameter('b', 2)
-
- p = Parameters()
- p.add_many(a, b)
-
- assert_(list(p.keys()) == ['a', 'b'])
-
- def test_expr_and_constraints_GH265(self):
- # test that parameters are reevaluated if they have bounds and expr
- # see GH265
- p = Parameters()
-
- p['a'] = Parameter('a', 10, True)
- p['b'] = Parameter('b', 10, True, 0, 20)
-
- p['a'].expr = '2 * b'
- assert_almost_equal(p['a'].value, 20)
-
- p['b'].value = 15
- assert_almost_equal(p['b'].value, 15)
- assert_almost_equal(p['a'].value, 30)
-
- p['b'].value = 30
- assert_almost_equal(p['b'].value, 20)
- assert_almost_equal(p['a'].value, 40)
-
- def test_pickle_parameter(self):
- # test that we can pickle a Parameter
- p = Parameter('a', 10, True, 0, 1)
- pkl = pickle.dumps(p)
-
- q = pickle.loads(pkl)
-
- assert_(p == q)
-
- def test_pickle_parameters(self):
- # test that we can pickle a Parameters object
- p = Parameters()
- p.add('a', 10, True, 0, 100)
- p.add('b', 10, True, 0, 100, 'a * sin(1)')
- p.update_constraints()
- p._asteval.symtable['abc'] = '2 * 3.142'
-
- pkl = pickle.dumps(p, -1)
- q = pickle.loads(pkl)
-
- q.update_constraints()
- assert_(p == q)
- assert_(not p is q)
-
- # now test if the asteval machinery survived
- assert_(q._asteval.symtable['abc'] == '2 * 3.142')
-
-
-if __name__ == '__main__':
- unittest.main()
+from __future__ import print_function
+from lmfit import Parameters, Parameter
+from lmfit.parameter import isclose
+from numpy.testing import assert_, assert_almost_equal, assert_equal
+import unittest
+from copy import deepcopy
+import numpy as np
+import pickle
+
+
+class TestParameters(unittest.TestCase):
+
+ def setUp(self):
+ self.params = Parameters()
+ self.params.add_many(('a', 1., True, None, None, None),
+ ('b', 2., True, None, None, None),
+ ('c', 3., True, None, None, '2. * a'))
+
+ def test_expr_was_evaluated(self):
+ self.params.update_constraints()
+ assert_almost_equal(self.params['c'].value,
+ 2 * self.params['a'].value)
+
+ def test_copy(self):
+ # check simple Parameters.copy() does not fail
+ # on non-trivial Parameters
+ p1 = Parameters()
+ p1.add('t', 2.0, min=0.0, max=5.0)
+ p1.add('x', 10.0)
+ p1.add('y', expr='x*t + sqrt(t)/3.0')
+
+ p2 = p1.copy()
+ assert(isinstance(p2, Parameters))
+ assert('t' in p2)
+ assert('y' in p2)
+ assert(p2['t'].max < 6.0)
+ assert(np.isinf(p2['x'].max) and p2['x'].max > 0)
+ assert(np.isinf(p2['x'].min) and p2['x'].min < 0)
+ assert('sqrt(t)' in p2['y'].expr )
+ assert(p2._asteval is not None)
+ assert(p2._asteval.symtable is not None)
+ assert((p2['y'].value > 20) and (p2['y'].value < 21))
+
+
+ def test_deepcopy(self):
+ # check that a simple copy works
+ b = deepcopy(self.params)
+ assert_(self.params == b)
+
+ # check that we can add a symbol to the interpreter
+ self.params['b'].expr = 'sin(1)'
+ self.params['b'].value = 10
+ assert_almost_equal(self.params['b'].value, np.sin(1))
+ assert_almost_equal(self.params._asteval.symtable['b'], np.sin(1))
+
+ # check that the symbols in the interpreter are still the same after
+ # deepcopying
+ b = deepcopy(self.params)
+
+ unique_symbols_params = self.params._asteval.user_defined_symbols()
+ unique_symbols_b = self.params._asteval.user_defined_symbols()
+ assert_(unique_symbols_b == unique_symbols_params)
+ for unique_symbol in unique_symbols_b:
+ if self.params._asteval.symtable[unique_symbol] is np.nan:
+ continue
+
+ assert_(self.params._asteval.symtable[unique_symbol]
+ ==
+ b._asteval.symtable[unique_symbol])
+
+ def test_add_many_params(self):
+ # test that we can add many parameters, but only parameters are added.
+ a = Parameter('a', 1)
+ b = Parameter('b', 2)
+
+ p = Parameters()
+ p.add_many(a, b)
+
+ assert_(list(p.keys()) == ['a', 'b'])
+
+ def test_expr_and_constraints_GH265(self):
+ # test that parameters are reevaluated if they have bounds and expr
+ # see GH265
+ p = Parameters()
+
+ p['a'] = Parameter('a', 10, True)
+ p['b'] = Parameter('b', 10, True, 0, 20)
+
+ assert_equal(p['b'].min, 0)
+ assert_equal(p['b'].max, 20)
+
+ p['a'].expr = '2 * b'
+ assert_almost_equal(p['a'].value, 20)
+
+ p['b'].value = 15
+ assert_almost_equal(p['b'].value, 15)
+ assert_almost_equal(p['a'].value, 30)
+
+ p['b'].value = 30
+ assert_almost_equal(p['b'].value, 20)
+ assert_almost_equal(p['a'].value, 40)
+
+ def test_pickle_parameter(self):
+ # test that we can pickle a Parameter
+ p = Parameter('a', 10, True, 0, 1)
+ pkl = pickle.dumps(p)
+
+ q = pickle.loads(pkl)
+
+ assert_(p == q)
+
+ def test_pickle_parameters(self):
+ # test that we can pickle a Parameters object
+ p = Parameters()
+ p.add('a', 10, True, 0, 100)
+ p.add('b', 10, True, 0, 100, 'a * sin(1)')
+ p.update_constraints()
+ p._asteval.symtable['abc'] = '2 * 3.142'
+
+ pkl = pickle.dumps(p, -1)
+ q = pickle.loads(pkl)
+
+ q.update_constraints()
+ assert_(p == q)
+ assert_(not p is q)
+
+ # now test if the asteval machinery survived
+ assert_(q._asteval.symtable['abc'] == '2 * 3.142')
+
+ # check that unpickling of Parameters is not affected by expr that
+ # refer to Parameter that are added later on. In the following
+ # example var_0.expr refers to var_1, which is a Parameter later
+ # on in the Parameters OrderedDict.
+ p = Parameters()
+ p.add('var_0', value=1)
+ p.add('var_1', value=2)
+ p['var_0'].expr = 'var_1'
+ pkl = pickle.dumps(p)
+ q = pickle.loads(pkl)
+
+ def test_isclose(self):
+ assert_(isclose(1., 1+1e-5, atol=1e-4, rtol=0))
+ assert_(not isclose(1., 1+1e-5, atol=1e-6, rtol=0))
+ assert_(isclose(1e10, 1.00001e10, rtol=1e-5, atol=1e-8))
+ assert_(not isclose(0, np.inf))
+ assert_(not isclose(-np.inf, np.inf))
+ assert_(isclose(np.inf, np.inf))
+ assert_(not isclose(np.nan, np.nan))
+
+
+if __name__ == '__main__':
+ unittest.main()
diff --git a/tests/test_params_set.py b/tests/test_params_set.py
index 26125ea..24b1089 100644
--- a/tests/test_params_set.py
+++ b/tests/test_params_set.py
@@ -1,48 +1,48 @@
-import numpy as np
-from numpy.testing import assert_allclose
-from lmfit import Parameters, minimize, report_fit
-from lmfit.lineshapes import gaussian
-from lmfit.models import VoigtModel
-
-def test_param_set():
- np.random.seed(2015)
- x = np.arange(0, 20, 0.05)
- y = gaussian(x, amplitude=15.43, center=4.5, sigma=2.13)
- y = y + 0.05 - 0.01*x + np.random.normal(scale=0.03, size=len(x))
-
- model = VoigtModel()
- params = model.guess(y, x=x)
-
- # test #1: gamma is constrained to equal sigma
- assert(params['gamma'].expr == 'sigma')
- params.update_constraints()
- sigval = params['gamma'].value
- assert_allclose(params['gamma'].value, sigval, 1e-4, 1e-4, '', True)
-
- # test #2: explicitly setting a param value should work, even when
- # it had been an expression. The value will be left as fixed
- gamval = 0.87543
- params['gamma'].set(value=gamval)
- assert(params['gamma'].expr is None)
- assert(not params['gamma'].vary)
- assert_allclose(params['gamma'].value, gamval, 1e-4, 1e-4, '', True)
-
- # test #3: explicitly setting an expression should work
- # Note, the only way to ensure that **ALL** constraints are up to date
- # is to call params.update_constraints(). This is because the constraint
- # may have multiple dependencies.
- params['gamma'].set(expr='sigma/2.0')
- assert(params['gamma'].expr is not None)
- assert(not params['gamma'].vary)
- params.update_constraints()
- assert_allclose(params['gamma'].value, sigval/2.0, 1e-4, 1e-4, '', True)
-
- # test #4: explicitly setting a param value WITH vary=True
- # will set it to be variable
- gamval = 0.7777
- params['gamma'].set(value=gamval, vary=True)
- assert(params['gamma'].expr is None)
- assert(params['gamma'].vary)
- assert_allclose(params['gamma'].value, gamval, 1e-4, 1e-4, '', True)
-
+import numpy as np
+from numpy.testing import assert_allclose
+from lmfit import Parameters, minimize, report_fit
+from lmfit.lineshapes import gaussian
+from lmfit.models import VoigtModel
+
+def test_param_set():
+ np.random.seed(2015)
+ x = np.arange(0, 20, 0.05)
+ y = gaussian(x, amplitude=15.43, center=4.5, sigma=2.13)
+ y = y + 0.05 - 0.01*x + np.random.normal(scale=0.03, size=len(x))
+
+ model = VoigtModel()
+ params = model.guess(y, x=x)
+
+ # test #1: gamma is constrained to equal sigma
+ assert(params['gamma'].expr == 'sigma')
+ params.update_constraints()
+ sigval = params['gamma'].value
+ assert_allclose(params['gamma'].value, sigval, 1e-4, 1e-4, '', True)
+
+ # test #2: explicitly setting a param value should work, even when
+ # it had been an expression. The value will be left as fixed
+ gamval = 0.87543
+ params['gamma'].set(value=gamval)
+ assert(params['gamma'].expr is None)
+ assert(not params['gamma'].vary)
+ assert_allclose(params['gamma'].value, gamval, 1e-4, 1e-4, '', True)
+
+ # test #3: explicitly setting an expression should work
+ # Note, the only way to ensure that **ALL** constraints are up to date
+ # is to call params.update_constraints(). This is because the constraint
+ # may have multiple dependencies.
+ params['gamma'].set(expr='sigma/2.0')
+ assert(params['gamma'].expr is not None)
+ assert(not params['gamma'].vary)
+ params.update_constraints()
+ assert_allclose(params['gamma'].value, sigval/2.0, 1e-4, 1e-4, '', True)
+
+ # test #4: explicitly setting a param value WITH vary=True
+ # will set it to be variable
+ gamval = 0.7777
+ params['gamma'].set(value=gamval, vary=True)
+ assert(params['gamma'].expr is None)
+ assert(params['gamma'].vary)
+ assert_allclose(params['gamma'].value, gamval, 1e-4, 1e-4, '', True)
+
test_param_set()
\ No newline at end of file
diff --git a/tests/test_stepmodel.py b/tests/test_stepmodel.py
index d854467..cabf118 100644
--- a/tests/test_stepmodel.py
+++ b/tests/test_stepmodel.py
@@ -1,58 +1,58 @@
-import numpy as np
-from lmfit import fit_report
-from lmfit.models import StepModel, ConstantModel
-from lmfit_testutils import assert_paramval, assert_paramattr
-
-def get_data():
- x = np.linspace(0, 10, 201)
- dat = np.ones_like(x)
- dat[:48] = 0.0
- dat[48:77] = np.arange(77-48)/(77.0-48)
- dat = dat + 5e-2*np.random.randn(len(x))
- dat = 110.2 * dat + 12.0
- return x, dat
-
-def test_stepmodel_linear():
- x, y = get_data()
- stepmod = StepModel(form='linear')
- const = ConstantModel()
- pars = stepmod.guess(y, x)
- pars = pars + const.make_params(c=3*y.min())
- mod = stepmod + const
-
- out = mod.fit(y, pars, x=x)
-
- assert(out.nfev > 5)
- assert(out.nvarys == 4)
- assert(out.chisqr > 1)
- assert(out.params['c'].value > 3)
- assert(out.params['center'].value > 1)
- assert(out.params['center'].value < 4)
- assert(out.params['sigma'].value > 0.5)
- assert(out.params['sigma'].value < 3.5)
- assert(out.params['amplitude'].value > 50)
-
-
-def test_stepmodel_erf():
- x, y = get_data()
- stepmod = StepModel(form='linear')
- const = ConstantModel()
- pars = stepmod.guess(y, x)
- pars = pars + const.make_params(c=3*y.min())
- mod = stepmod + const
-
- out = mod.fit(y, pars, x=x)
-
- assert(out.nfev > 5)
- assert(out.nvarys == 4)
- assert(out.chisqr > 1)
- assert(out.params['c'].value > 3)
- assert(out.params['center'].value > 1)
- assert(out.params['center'].value < 4)
- assert(out.params['amplitude'].value > 50)
- assert(out.params['sigma'].value > 0.2)
- assert(out.params['sigma'].value < 1.5)
-
-if __name__ == '__main__':
- # test_stepmodel_linear()
- test_stepmodel_erf()
+import numpy as np
+from lmfit import fit_report
+from lmfit.models import StepModel, ConstantModel
+from lmfit_testutils import assert_paramval, assert_paramattr
+
+def get_data():
+ x = np.linspace(0, 10, 201)
+ dat = np.ones_like(x)
+ dat[:48] = 0.0
+ dat[48:77] = np.arange(77-48)/(77.0-48)
+ dat = dat + 5e-2*np.random.randn(len(x))
+ dat = 110.2 * dat + 12.0
+ return x, dat
+
+def test_stepmodel_linear():
+ x, y = get_data()
+ stepmod = StepModel(form='linear')
+ const = ConstantModel()
+ pars = stepmod.guess(y, x)
+ pars = pars + const.make_params(c=3*y.min())
+ mod = stepmod + const
+
+ out = mod.fit(y, pars, x=x)
+
+ assert(out.nfev > 5)
+ assert(out.nvarys == 4)
+ assert(out.chisqr > 1)
+ assert(out.params['c'].value > 3)
+ assert(out.params['center'].value > 1)
+ assert(out.params['center'].value < 4)
+ assert(out.params['sigma'].value > 0.5)
+ assert(out.params['sigma'].value < 3.5)
+ assert(out.params['amplitude'].value > 50)
+
+
+def test_stepmodel_erf():
+ x, y = get_data()
+ stepmod = StepModel(form='linear')
+ const = ConstantModel()
+ pars = stepmod.guess(y, x)
+ pars = pars + const.make_params(c=3*y.min())
+ mod = stepmod + const
+
+ out = mod.fit(y, pars, x=x)
+
+ assert(out.nfev > 5)
+ assert(out.nvarys == 4)
+ assert(out.chisqr > 1)
+ assert(out.params['c'].value > 3)
+ assert(out.params['center'].value > 1)
+ assert(out.params['center'].value < 4)
+ assert(out.params['amplitude'].value > 50)
+ assert(out.params['sigma'].value > 0.2)
+ assert(out.params['sigma'].value < 1.5)
+
+if __name__ == '__main__':
+ # test_stepmodel_linear()
+ test_stepmodel_erf()
diff --git a/versioneer.py b/versioneer.py
index 4162e8a..481180d 100644
--- a/versioneer.py
+++ b/versioneer.py
@@ -1,901 +1,901 @@
-
-# Version: 0.12
-
-"""
-The Versioneer
-==============
-
-* like a rocketeer, but for versions!
-* https://github.com/warner/python-versioneer
-* Brian Warner
-* License: Public Domain
-* Compatible With: python2.6, 2.7, 3.2, 3.3, 3.4, and pypy
-
-[](https://travis-ci.org/warner/python-versioneer)
-
-This is a tool for managing a recorded version number in distutils-based
-python projects. The goal is to remove the tedious and error-prone "update
-the embedded version string" step from your release process. Making a new
-release should be as easy as recording a new tag in your version-control
-system, and maybe making new tarballs.
-
-
-## Quick Install
-
-* `pip install versioneer` to somewhere to your $PATH
-* run `versioneer-installer` in your source tree: this installs `versioneer.py`
-* follow the instructions below (also in the `versioneer.py` docstring)
-
-## Version Identifiers
-
-Source trees come from a variety of places:
-
-* a version-control system checkout (mostly used by developers)
-* a nightly tarball, produced by build automation
-* a snapshot tarball, produced by a web-based VCS browser, like github's
- "tarball from tag" feature
-* a release tarball, produced by "setup.py sdist", distributed through PyPI
-
-Within each source tree, the version identifier (either a string or a number,
-this tool is format-agnostic) can come from a variety of places:
-
-* ask the VCS tool itself, e.g. "git describe" (for checkouts), which knows
- about recent "tags" and an absolute revision-id
-* the name of the directory into which the tarball was unpacked
-* an expanded VCS keyword ($Id$, etc)
-* a `_version.py` created by some earlier build step
-
-For released software, the version identifier is closely related to a VCS
-tag. Some projects use tag names that include more than just the version
-string (e.g. "myproject-1.2" instead of just "1.2"), in which case the tool
-needs to strip the tag prefix to extract the version identifier. For
-unreleased software (between tags), the version identifier should provide
-enough information to help developers recreate the same tree, while also
-giving them an idea of roughly how old the tree is (after version 1.2, before
-version 1.3). Many VCS systems can report a description that captures this,
-for example 'git describe --tags --dirty --always' reports things like
-"0.7-1-g574ab98-dirty" to indicate that the checkout is one revision past the
-0.7 tag, has a unique revision id of "574ab98", and is "dirty" (it has
-uncommitted changes.
-
-The version identifier is used for multiple purposes:
-
-* to allow the module to self-identify its version: `myproject.__version__`
-* to choose a name and prefix for a 'setup.py sdist' tarball
-
-## Theory of Operation
-
-Versioneer works by adding a special `_version.py` file into your source
-tree, where your `__init__.py` can import it. This `_version.py` knows how to
-dynamically ask the VCS tool for version information at import time. However,
-when you use "setup.py build" or "setup.py sdist", `_version.py` in the new
-copy is replaced by a small static file that contains just the generated
-version data.
-
-`_version.py` also contains `$Revision$` markers, and the installation
-process marks `_version.py` to have this marker rewritten with a tag name
-during the "git archive" command. As a result, generated tarballs will
-contain enough information to get the proper version.
-
-
-## Installation
-
-First, decide on values for the following configuration variables:
-
-* `VCS`: the version control system you use. Currently accepts "git".
-
-* `versionfile_source`:
-
- A project-relative pathname into which the generated version strings should
- be written. This is usually a `_version.py` next to your project's main
- `__init__.py` file, so it can be imported at runtime. If your project uses
- `src/myproject/__init__.py`, this should be `src/myproject/_version.py`.
- This file should be checked in to your VCS as usual: the copy created below
- by `setup.py versioneer` will include code that parses expanded VCS
- keywords in generated tarballs. The 'build' and 'sdist' commands will
- replace it with a copy that has just the calculated version string.
-
- This must be set even if your project does not have any modules (and will
- therefore never import `_version.py`), since "setup.py sdist" -based trees
- still need somewhere to record the pre-calculated version strings. Anywhere
- in the source tree should do. If there is a `__init__.py` next to your
- `_version.py`, the `setup.py versioneer` command (described below) will
- append some `__version__`-setting assignments, if they aren't already
- present.
-
-* `versionfile_build`:
-
- Like `versionfile_source`, but relative to the build directory instead of
- the source directory. These will differ when your setup.py uses
- 'package_dir='. If you have `package_dir={'myproject': 'src/myproject'}`,
- then you will probably have `versionfile_build='myproject/_version.py'` and
- `versionfile_source='src/myproject/_version.py'`.
-
- If this is set to None, then `setup.py build` will not attempt to rewrite
- any `_version.py` in the built tree. If your project does not have any
- libraries (e.g. if it only builds a script), then you should use
- `versionfile_build = None` and override `distutils.command.build_scripts`
- to explicitly insert a copy of `versioneer.get_version()` into your
- generated script.
-
-* `tag_prefix`:
-
- a string, like 'PROJECTNAME-', which appears at the start of all VCS tags.
- If your tags look like 'myproject-1.2.0', then you should use
- tag_prefix='myproject-'. If you use unprefixed tags like '1.2.0', this
- should be an empty string.
-
-* `parentdir_prefix`:
-
- a string, frequently the same as tag_prefix, which appears at the start of
- all unpacked tarball filenames. If your tarball unpacks into
- 'myproject-1.2.0', this should be 'myproject-'.
-
-This tool provides one script, named `versioneer-installer`. That script does
-one thing: write a copy of `versioneer.py` into the current directory.
-
-To versioneer-enable your project:
-
-* 1: Run `versioneer-installer` to copy `versioneer.py` into the top of your
- source tree.
-
-* 2: add the following lines to the top of your `setup.py`, with the
- configuration values you decided earlier:
-
- import versioneer
- versioneer.VCS = 'git'
- versioneer.versionfile_source = 'src/myproject/_version.py'
- versioneer.versionfile_build = 'myproject/_version.py'
- versioneer.tag_prefix = '' # tags are like 1.2.0
- versioneer.parentdir_prefix = 'myproject-' # dirname like 'myproject-1.2.0'
-
-* 3: add the following arguments to the setup() call in your setup.py:
-
- version=versioneer.get_version(),
- cmdclass=versioneer.get_cmdclass(),
-
-* 4: now run `setup.py versioneer`, which will create `_version.py`, and will
- modify your `__init__.py` (if one exists next to `_version.py`) to define
- `__version__` (by calling a function from `_version.py`). It will also
- modify your `MANIFEST.in` to include both `versioneer.py` and the generated
- `_version.py` in sdist tarballs.
-
-* 5: commit these changes to your VCS. To make sure you won't forget,
- `setup.py versioneer` will mark everything it touched for addition.
-
-## Post-Installation Usage
-
-Once established, all uses of your tree from a VCS checkout should get the
-current version string. All generated tarballs should include an embedded
-version string (so users who unpack them will not need a VCS tool installed).
-
-If you distribute your project through PyPI, then the release process should
-boil down to two steps:
-
-* 1: git tag 1.0
-* 2: python setup.py register sdist upload
-
-If you distribute it through github (i.e. users use github to generate
-tarballs with `git archive`), the process is:
-
-* 1: git tag 1.0
-* 2: git push; git push --tags
-
-Currently, all version strings must be based upon a tag. Versioneer will
-report "unknown" until your tree has at least one tag in its history. This
-restriction will be fixed eventually (see issue #12).
-
-## Version-String Flavors
-
-Code which uses Versioneer can learn about its version string at runtime by
-importing `_version` from your main `__init__.py` file and running the
-`get_versions()` function. From the "outside" (e.g. in `setup.py`), you can
-import the top-level `versioneer.py` and run `get_versions()`.
-
-Both functions return a dictionary with different keys for different flavors
-of the version string:
-
-* `['version']`: condensed tag+distance+shortid+dirty identifier. For git,
- this uses the output of `git describe --tags --dirty --always` but strips
- the tag_prefix. For example "0.11-2-g1076c97-dirty" indicates that the tree
- is like the "1076c97" commit but has uncommitted changes ("-dirty"), and
- that this commit is two revisions ("-2-") beyond the "0.11" tag. For
- released software (exactly equal to a known tag), the identifier will only
- contain the stripped tag, e.g. "0.11".
-
-* `['full']`: detailed revision identifier. For Git, this is the full SHA1
- commit id, followed by "-dirty" if the tree contains uncommitted changes,
- e.g. "1076c978a8d3cfc70f408fe5974aa6c092c949ac-dirty".
-
-Some variants are more useful than others. Including `full` in a bug report
-should allow developers to reconstruct the exact code being tested (or
-indicate the presence of local changes that should be shared with the
-developers). `version` is suitable for display in an "about" box or a CLI
-`--version` output: it can be easily compared against release notes and lists
-of bugs fixed in various releases.
-
-In the future, this will also include a
-[PEP-0440](http://legacy.python.org/dev/peps/pep-0440/) -compatible flavor
-(e.g. `1.2.post0.dev123`). This loses a lot of information (and has no room
-for a hash-based revision id), but is safe to use in a `setup.py`
-"`version=`" argument. It also enables tools like *pip* to compare version
-strings and evaluate compatibility constraint declarations.
-
-The `setup.py versioneer` command adds the following text to your
-`__init__.py` to place a basic version in `YOURPROJECT.__version__`:
-
- from ._version import get_versions
- __version__ = get_versions()['version']
- del get_versions
-
-## Updating Versioneer
-
-To upgrade your project to a new release of Versioneer, do the following:
-
-* install the new Versioneer (`pip install -U versioneer` or equivalent)
-* re-run `versioneer-installer` in your source tree to replace your copy of
- `versioneer.py`
-* edit `setup.py`, if necessary, to include any new configuration settings
- indicated by the release notes
-* re-run `setup.py versioneer` to replace `SRC/_version.py`
-* commit any changed files
-
-### Upgrading from 0.10 to 0.11
-
-You must add a `versioneer.VCS = "git"` to your `setup.py` before re-running
-`setup.py versioneer`. This will enable the use of additional version-control
-systems (SVN, etc) in the future.
-
-### Upgrading from 0.11 to 0.12
-
-Nothing special.
-
-## Future Directions
-
-This tool is designed to make it easily extended to other version-control
-systems: all VCS-specific components are in separate directories like
-src/git/ . The top-level `versioneer.py` script is assembled from these
-components by running make-versioneer.py . In the future, make-versioneer.py
-will take a VCS name as an argument, and will construct a version of
-`versioneer.py` that is specific to the given VCS. It might also take the
-configuration arguments that are currently provided manually during
-installation by editing setup.py . Alternatively, it might go the other
-direction and include code from all supported VCS systems, reducing the
-number of intermediate scripts.
-
-
-## License
-
-To make Versioneer easier to embed, all its code is hereby released into the
-public domain. The `_version.py` that it creates is also in the public
-domain.
-
-"""
-
-import os, sys, re, subprocess, errno
-from distutils.core import Command
-from distutils.command.sdist import sdist as _sdist
-from distutils.command.build import build as _build
-
-# these configuration settings will be overridden by setup.py after it
-# imports us
-versionfile_source = None
-versionfile_build = None
-tag_prefix = None
-parentdir_prefix = None
-VCS = None
-
-# these dictionaries contain VCS-specific tools
-LONG_VERSION_PY = {}
-
-def run_command(commands, args, cwd=None, verbose=False, hide_stderr=False):
- assert isinstance(commands, list)
- p = None
- for c in commands:
- try:
- # remember shell=False, so use git.cmd on windows, not just git
- p = subprocess.Popen([c] + args, cwd=cwd, stdout=subprocess.PIPE,
- stderr=(subprocess.PIPE if hide_stderr
- else None))
- break
- except EnvironmentError:
- e = sys.exc_info()[1]
- if e.errno == errno.ENOENT:
- continue
- if verbose:
- print("unable to run %s" % args[0])
- print(e)
- return None
- else:
- if verbose:
- print("unable to find command, tried %s" % (commands,))
- return None
- stdout = p.communicate()[0].strip()
- if sys.version >= '3':
- stdout = stdout.decode()
- if p.returncode != 0:
- if verbose:
- print("unable to run %s (error)" % args[0])
- return None
- return stdout
-
-LONG_VERSION_PY['git'] = '''
-# This file helps to compute a version number in source trees obtained from
-# git-archive tarball (such as those provided by githubs download-from-tag
-# feature). Distribution tarballs (built by setup.py sdist) and build
-# directories (produced by setup.py build) will contain a much shorter file
-# that just contains the computed version number.
-
-# This file is released into the public domain. Generated by
-# versioneer-0.12 (https://github.com/warner/python-versioneer)
-
-# these strings will be replaced by git during git-archive
-git_refnames = "%(DOLLAR)sFormat:%%d%(DOLLAR)s"
-git_full = "%(DOLLAR)sFormat:%%H%(DOLLAR)s"
-
-# these strings are filled in when 'setup.py versioneer' creates _version.py
-tag_prefix = "%(TAG_PREFIX)s"
-parentdir_prefix = "%(PARENTDIR_PREFIX)s"
-versionfile_source = "%(VERSIONFILE_SOURCE)s"
-
-import os, sys, re, subprocess, errno
-
-def run_command(commands, args, cwd=None, verbose=False, hide_stderr=False):
- assert isinstance(commands, list)
- p = None
- for c in commands:
- try:
- # remember shell=False, so use git.cmd on windows, not just git
- p = subprocess.Popen([c] + args, cwd=cwd, stdout=subprocess.PIPE,
- stderr=(subprocess.PIPE if hide_stderr
- else None))
- break
- except EnvironmentError:
- e = sys.exc_info()[1]
- if e.errno == errno.ENOENT:
- continue
- if verbose:
- print("unable to run %%s" %% args[0])
- print(e)
- return None
- else:
- if verbose:
- print("unable to find command, tried %%s" %% (commands,))
- return None
- stdout = p.communicate()[0].strip()
- if sys.version >= '3':
- stdout = stdout.decode()
- if p.returncode != 0:
- if verbose:
- print("unable to run %%s (error)" %% args[0])
- return None
- return stdout
-
-
-def versions_from_parentdir(parentdir_prefix, root, verbose=False):
- # Source tarballs conventionally unpack into a directory that includes
- # both the project name and a version string.
- dirname = os.path.basename(root)
- if not dirname.startswith(parentdir_prefix):
- if verbose:
- print("guessing rootdir is '%%s', but '%%s' doesn't start with prefix '%%s'" %%
- (root, dirname, parentdir_prefix))
- return None
- return {"version": dirname[len(parentdir_prefix):], "full": ""}
-
-def git_get_keywords(versionfile_abs):
- # the code embedded in _version.py can just fetch the value of these
- # keywords. When used from setup.py, we don't want to import _version.py,
- # so we do it with a regexp instead. This function is not used from
- # _version.py.
- keywords = {}
- try:
- f = open(versionfile_abs,"r")
- for line in f.readlines():
- if line.strip().startswith("git_refnames ="):
- mo = re.search(r'=\s*"(.*)"', line)
- if mo:
- keywords["refnames"] = mo.group(1)
- if line.strip().startswith("git_full ="):
- mo = re.search(r'=\s*"(.*)"', line)
- if mo:
- keywords["full"] = mo.group(1)
- f.close()
- except EnvironmentError:
- pass
- return keywords
-
-def git_versions_from_keywords(keywords, tag_prefix, verbose=False):
- if not keywords:
- return {} # keyword-finding function failed to find keywords
- refnames = keywords["refnames"].strip()
- if refnames.startswith("$Format"):
- if verbose:
- print("keywords are unexpanded, not using")
- return {} # unexpanded, so not in an unpacked git-archive tarball
- refs = set([r.strip() for r in refnames.strip("()").split(",")])
- # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of
- # just "foo-1.0". If we see a "tag: " prefix, prefer those.
- TAG = "tag: "
- tags = set([r[len(TAG):] for r in refs if r.startswith(TAG)])
- if not tags:
- # Either we're using git < 1.8.3, or there really are no tags. We use
- # a heuristic: assume all version tags have a digit. The old git %%d
- # expansion behaves like git log --decorate=short and strips out the
- # refs/heads/ and refs/tags/ prefixes that would let us distinguish
- # between branches and tags. By ignoring refnames without digits, we
- # filter out many common branch names like "release" and
- # "stabilization", as well as "HEAD" and "master".
- tags = set([r for r in refs if re.search(r'\d', r)])
- if verbose:
- print("discarding '%%s', no digits" %% ",".join(refs-tags))
- if verbose:
- print("likely tags: %%s" %% ",".join(sorted(tags)))
- for ref in sorted(tags):
- # sorting will prefer e.g. "2.0" over "2.0rc1"
- if ref.startswith(tag_prefix):
- r = ref[len(tag_prefix):]
- if verbose:
- print("picking %%s" %% r)
- return { "version": r,
- "full": keywords["full"].strip() }
- # no suitable tags, so we use the full revision id
- if verbose:
- print("no suitable tags, using full revision id")
- return { "version": keywords["full"].strip(),
- "full": keywords["full"].strip() }
-
-
-def git_versions_from_vcs(tag_prefix, root, verbose=False):
- # this runs 'git' from the root of the source tree. This only gets called
- # if the git-archive 'subst' keywords were *not* expanded, and
- # _version.py hasn't already been rewritten with a short version string,
- # meaning we're inside a checked out source tree.
-
- if not os.path.exists(os.path.join(root, ".git")):
- if verbose:
- print("no .git in %%s" %% root)
- return {}
-
- GITS = ["git"]
- if sys.platform == "win32":
- GITS = ["git.cmd", "git.exe"]
- stdout = run_command(GITS, ["describe", "--tags", "--dirty", "--always"],
- cwd=root)
- if stdout is None:
- return {}
- if not stdout.startswith(tag_prefix):
- if verbose:
- print("tag '%%s' doesn't start with prefix '%%s'" %% (stdout, tag_prefix))
- return {}
- tag = stdout[len(tag_prefix):]
- stdout = run_command(GITS, ["rev-parse", "HEAD"], cwd=root)
- if stdout is None:
- return {}
- full = stdout.strip()
- if tag.endswith("-dirty"):
- full += "-dirty"
- return {"version": tag, "full": full}
-
-
-def get_versions(default={"version": "unknown", "full": ""}, verbose=False):
- # I am in _version.py, which lives at ROOT/VERSIONFILE_SOURCE. If we have
- # __file__, we can work backwards from there to the root. Some
- # py2exe/bbfreeze/non-CPython implementations don't do __file__, in which
- # case we can only use expanded keywords.
-
- keywords = { "refnames": git_refnames, "full": git_full }
- ver = git_versions_from_keywords(keywords, tag_prefix, verbose)
- if ver:
- return ver
-
- try:
- root = os.path.abspath(__file__)
- # versionfile_source is the relative path from the top of the source
- # tree (where the .git directory might live) to this file. Invert
- # this to find the root from __file__.
- for i in range(len(versionfile_source.split(os.sep))):
- root = os.path.dirname(root)
- except NameError:
- return default
-
- return (git_versions_from_vcs(tag_prefix, root, verbose)
- or versions_from_parentdir(parentdir_prefix, root, verbose)
- or default)
-'''
-
-def git_get_keywords(versionfile_abs):
- # the code embedded in _version.py can just fetch the value of these
- # keywords. When used from setup.py, we don't want to import _version.py,
- # so we do it with a regexp instead. This function is not used from
- # _version.py.
- keywords = {}
- try:
- f = open(versionfile_abs,"r")
- for line in f.readlines():
- if line.strip().startswith("git_refnames ="):
- mo = re.search(r'=\s*"(.*)"', line)
- if mo:
- keywords["refnames"] = mo.group(1)
- if line.strip().startswith("git_full ="):
- mo = re.search(r'=\s*"(.*)"', line)
- if mo:
- keywords["full"] = mo.group(1)
- f.close()
- except EnvironmentError:
- pass
- return keywords
-
-def git_versions_from_keywords(keywords, tag_prefix, verbose=False):
- if not keywords:
- return {} # keyword-finding function failed to find keywords
- refnames = keywords["refnames"].strip()
- if refnames.startswith("$Format"):
- if verbose:
- print("keywords are unexpanded, not using")
- return {} # unexpanded, so not in an unpacked git-archive tarball
- refs = set([r.strip() for r in refnames.strip("()").split(",")])
- # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of
- # just "foo-1.0". If we see a "tag: " prefix, prefer those.
- TAG = "tag: "
- tags = set([r[len(TAG):] for r in refs if r.startswith(TAG)])
- if not tags:
- # Either we're using git < 1.8.3, or there really are no tags. We use
- # a heuristic: assume all version tags have a digit. The old git %d
- # expansion behaves like git log --decorate=short and strips out the
- # refs/heads/ and refs/tags/ prefixes that would let us distinguish
- # between branches and tags. By ignoring refnames without digits, we
- # filter out many common branch names like "release" and
- # "stabilization", as well as "HEAD" and "master".
- tags = set([r for r in refs if re.search(r'\d', r)])
- if verbose:
- print("discarding '%s', no digits" % ",".join(refs-tags))
- if verbose:
- print("likely tags: %s" % ",".join(sorted(tags)))
- for ref in sorted(tags):
- # sorting will prefer e.g. "2.0" over "2.0rc1"
- if ref.startswith(tag_prefix):
- r = ref[len(tag_prefix):]
- if verbose:
- print("picking %s" % r)
- return { "version": r,
- "full": keywords["full"].strip() }
- # no suitable tags, so we use the full revision id
- if verbose:
- print("no suitable tags, using full revision id")
- return { "version": keywords["full"].strip(),
- "full": keywords["full"].strip() }
-
-
-def git_versions_from_vcs(tag_prefix, root, verbose=False):
- # this runs 'git' from the root of the source tree. This only gets called
- # if the git-archive 'subst' keywords were *not* expanded, and
- # _version.py hasn't already been rewritten with a short version string,
- # meaning we're inside a checked out source tree.
-
- if not os.path.exists(os.path.join(root, ".git")):
- if verbose:
- print("no .git in %s" % root)
- return {}
-
- GITS = ["git"]
- if sys.platform == "win32":
- GITS = ["git.cmd", "git.exe"]
- stdout = run_command(GITS, ["describe", "--tags", "--dirty", "--always"],
- cwd=root)
- if stdout is None:
- return {}
- if not stdout.startswith(tag_prefix):
- if verbose:
- print("tag '%s' doesn't start with prefix '%s'" % (stdout, tag_prefix))
- return {}
- tag = stdout[len(tag_prefix):]
- stdout = run_command(GITS, ["rev-parse", "HEAD"], cwd=root)
- if stdout is None:
- return {}
- full = stdout.strip()
- if tag.endswith("-dirty"):
- full += "-dirty"
- return {"version": tag, "full": full}
-
-
-def do_vcs_install(manifest_in, versionfile_source, ipy):
- GITS = ["git"]
- if sys.platform == "win32":
- GITS = ["git.cmd", "git.exe"]
- files = [manifest_in, versionfile_source]
- if ipy:
- files.append(ipy)
- try:
- me = __file__
- if me.endswith(".pyc") or me.endswith(".pyo"):
- me = os.path.splitext(me)[0] + ".py"
- versioneer_file = os.path.relpath(me)
- except NameError:
- versioneer_file = "versioneer.py"
- files.append(versioneer_file)
- present = False
- try:
- f = open(".gitattributes", "r")
- for line in f.readlines():
- if line.strip().startswith(versionfile_source):
- if "export-subst" in line.strip().split()[1:]:
- present = True
- f.close()
- except EnvironmentError:
- pass
- if not present:
- f = open(".gitattributes", "a+")
- f.write("%s export-subst\n" % versionfile_source)
- f.close()
- files.append(".gitattributes")
- run_command(GITS, ["add", "--"] + files)
-
-def versions_from_parentdir(parentdir_prefix, root, verbose=False):
- # Source tarballs conventionally unpack into a directory that includes
- # both the project name and a version string.
- dirname = os.path.basename(root)
- if not dirname.startswith(parentdir_prefix):
- if verbose:
- print("guessing rootdir is '%s', but '%s' doesn't start with prefix '%s'" %
- (root, dirname, parentdir_prefix))
- return None
- return {"version": dirname[len(parentdir_prefix):], "full": ""}
-
-SHORT_VERSION_PY = """
-# This file was generated by 'versioneer.py' (0.12) from
-# revision-control system data, or from the parent directory name of an
-# unpacked source archive. Distribution tarballs contain a pre-generated copy
-# of this file.
-
-version_version = '%(version)s'
-version_full = '%(full)s'
-def get_versions(default={}, verbose=False):
- return {'version': version_version, 'full': version_full}
-
-"""
-
-DEFAULT = {"version": "unknown", "full": "unknown"}
-
-def versions_from_file(filename):
- versions = {}
- try:
- with open(filename) as f:
- for line in f.readlines():
- mo = re.match("version_version = '([^']+)'", line)
- if mo:
- versions["version"] = mo.group(1)
- mo = re.match("version_full = '([^']+)'", line)
- if mo:
- versions["full"] = mo.group(1)
- except EnvironmentError:
- return {}
-
- return versions
-
-def write_to_version_file(filename, versions):
- with open(filename, "w") as f:
- f.write(SHORT_VERSION_PY % versions)
-
- print("set %s to '%s'" % (filename, versions["version"]))
-
-
-def get_root():
- try:
- return os.path.dirname(os.path.abspath(__file__))
- except NameError:
- return os.path.dirname(os.path.abspath(sys.argv[0]))
-
-def vcs_function(vcs, suffix):
- return getattr(sys.modules[__name__], '%s_%s' % (vcs, suffix), None)
-
-def get_versions(default=DEFAULT, verbose=False):
- # returns dict with two keys: 'version' and 'full'
- assert versionfile_source is not None, "please set versioneer.versionfile_source"
- assert tag_prefix is not None, "please set versioneer.tag_prefix"
- assert parentdir_prefix is not None, "please set versioneer.parentdir_prefix"
- assert VCS is not None, "please set versioneer.VCS"
-
- # I am in versioneer.py, which must live at the top of the source tree,
- # which we use to compute the root directory. py2exe/bbfreeze/non-CPython
- # don't have __file__, in which case we fall back to sys.argv[0] (which
- # ought to be the setup.py script). We prefer __file__ since that's more
- # robust in cases where setup.py was invoked in some weird way (e.g. pip)
- root = get_root()
- versionfile_abs = os.path.join(root, versionfile_source)
-
- # extract version from first of _version.py, VCS command (e.g. 'git
- # describe'), parentdir. This is meant to work for developers using a
- # source checkout, for users of a tarball created by 'setup.py sdist',
- # and for users of a tarball/zipball created by 'git archive' or github's
- # download-from-tag feature or the equivalent in other VCSes.
-
- get_keywords_f = vcs_function(VCS, "get_keywords")
- versions_from_keywords_f = vcs_function(VCS, "versions_from_keywords")
- if get_keywords_f and versions_from_keywords_f:
- vcs_keywords = get_keywords_f(versionfile_abs)
- ver = versions_from_keywords_f(vcs_keywords, tag_prefix)
- if ver:
- if verbose: print("got version from expanded keyword %s" % ver)
- return ver
-
- ver = versions_from_file(versionfile_abs)
- if ver:
- if verbose: print("got version from file %s %s" % (versionfile_abs,ver))
- return ver
-
- versions_from_vcs_f = vcs_function(VCS, "versions_from_vcs")
- if versions_from_vcs_f:
- ver = versions_from_vcs_f(tag_prefix, root, verbose)
- if ver:
- if verbose: print("got version from VCS %s" % ver)
- return ver
-
- ver = versions_from_parentdir(parentdir_prefix, root, verbose)
- if ver:
- if verbose: print("got version from parentdir %s" % ver)
- return ver
-
- if verbose: print("got version from default %s" % default)
- return default
-
-def get_version(verbose=False):
- return get_versions(verbose=verbose)["version"]
-
-class cmd_version(Command):
- description = "report generated version string"
- user_options = []
- boolean_options = []
- def initialize_options(self):
- pass
- def finalize_options(self):
- pass
- def run(self):
- ver = get_version(verbose=True)
- print("Version is currently: %s" % ver)
-
-
-class cmd_build(_build):
- def run(self):
- versions = get_versions(verbose=True)
- _build.run(self)
- # now locate _version.py in the new build/ directory and replace it
- # with an updated value
- if versionfile_build:
- target_versionfile = os.path.join(self.build_lib, versionfile_build)
- print("UPDATING %s" % target_versionfile)
- os.unlink(target_versionfile)
- with open(target_versionfile, "w") as f:
- f.write(SHORT_VERSION_PY % versions)
-
-if 'cx_Freeze' in sys.modules: # cx_freeze enabled?
- from cx_Freeze.dist import build_exe as _build_exe
-
- class cmd_build_exe(_build_exe):
- def run(self):
- versions = get_versions(verbose=True)
- target_versionfile = versionfile_source
- print("UPDATING %s" % target_versionfile)
- os.unlink(target_versionfile)
- with open(target_versionfile, "w") as f:
- f.write(SHORT_VERSION_PY % versions)
-
- _build_exe.run(self)
- os.unlink(target_versionfile)
- with open(versionfile_source, "w") as f:
- assert VCS is not None, "please set versioneer.VCS"
- LONG = LONG_VERSION_PY[VCS]
- f.write(LONG % {"DOLLAR": "$",
- "TAG_PREFIX": tag_prefix,
- "PARENTDIR_PREFIX": parentdir_prefix,
- "VERSIONFILE_SOURCE": versionfile_source,
- })
-
-class cmd_sdist(_sdist):
- def run(self):
- versions = get_versions(verbose=True)
- self._versioneer_generated_versions = versions
- # unless we update this, the command will keep using the old version
- self.distribution.metadata.version = versions["version"]
- return _sdist.run(self)
-
- def make_release_tree(self, base_dir, files):
- _sdist.make_release_tree(self, base_dir, files)
- # now locate _version.py in the new base_dir directory (remembering
- # that it may be a hardlink) and replace it with an updated value
- target_versionfile = os.path.join(base_dir, versionfile_source)
- print("UPDATING %s" % target_versionfile)
- os.unlink(target_versionfile)
- with open(target_versionfile, "w") as f:
- f.write(SHORT_VERSION_PY % self._versioneer_generated_versions)
-
-INIT_PY_SNIPPET = """
-from ._version import get_versions
-__version__ = get_versions()['version']
-del get_versions
-"""
-
-class cmd_update_files(Command):
- description = "install/upgrade Versioneer files: __init__.py SRC/_version.py"
- user_options = []
- boolean_options = []
- def initialize_options(self):
- pass
- def finalize_options(self):
- pass
- def run(self):
- print(" creating %s" % versionfile_source)
- with open(versionfile_source, "w") as f:
- assert VCS is not None, "please set versioneer.VCS"
- LONG = LONG_VERSION_PY[VCS]
- f.write(LONG % {"DOLLAR": "$",
- "TAG_PREFIX": tag_prefix,
- "PARENTDIR_PREFIX": parentdir_prefix,
- "VERSIONFILE_SOURCE": versionfile_source,
- })
-
- ipy = os.path.join(os.path.dirname(versionfile_source), "__init__.py")
- if os.path.exists(ipy):
- try:
- with open(ipy, "r") as f:
- old = f.read()
- except EnvironmentError:
- old = ""
- if INIT_PY_SNIPPET not in old:
- print(" appending to %s" % ipy)
- with open(ipy, "a") as f:
- f.write(INIT_PY_SNIPPET)
- else:
- print(" %s unmodified" % ipy)
- else:
- print(" %s doesn't exist, ok" % ipy)
- ipy = None
-
- # Make sure both the top-level "versioneer.py" and versionfile_source
- # (PKG/_version.py, used by runtime code) are in MANIFEST.in, so
- # they'll be copied into source distributions. Pip won't be able to
- # install the package without this.
- manifest_in = os.path.join(get_root(), "MANIFEST.in")
- simple_includes = set()
- try:
- with open(manifest_in, "r") as f:
- for line in f:
- if line.startswith("include "):
- for include in line.split()[1:]:
- simple_includes.add(include)
- except EnvironmentError:
- pass
- # That doesn't cover everything MANIFEST.in can do
- # (http://docs.python.org/2/distutils/sourcedist.html#commands), so
- # it might give some false negatives. Appending redundant 'include'
- # lines is safe, though.
- if "versioneer.py" not in simple_includes:
- print(" appending 'versioneer.py' to MANIFEST.in")
- with open(manifest_in, "a") as f:
- f.write("include versioneer.py\n")
- else:
- print(" 'versioneer.py' already in MANIFEST.in")
- if versionfile_source not in simple_includes:
- print(" appending versionfile_source ('%s') to MANIFEST.in" %
- versionfile_source)
- with open(manifest_in, "a") as f:
- f.write("include %s\n" % versionfile_source)
- else:
- print(" versionfile_source already in MANIFEST.in")
-
- # Make VCS-specific changes. For git, this means creating/changing
- # .gitattributes to mark _version.py for export-time keyword
- # substitution.
- do_vcs_install(manifest_in, versionfile_source, ipy)
-
-def get_cmdclass():
- cmds = {'version': cmd_version,
- 'versioneer': cmd_update_files,
- 'build': cmd_build,
- 'sdist': cmd_sdist,
- }
- if 'cx_Freeze' in sys.modules: # cx_freeze enabled?
- cmds['build_exe'] = cmd_build_exe
- del cmds['build']
-
- return cmds
+
+# Version: 0.12
+
+"""
+The Versioneer
+==============
+
+* like a rocketeer, but for versions!
+* https://github.com/warner/python-versioneer
+* Brian Warner
+* License: Public Domain
+* Compatible With: python2.6, 2.7, 3.2, 3.3, 3.4, and pypy
+
+[](https://travis-ci.org/warner/python-versioneer)
+
+This is a tool for managing a recorded version number in distutils-based
+python projects. The goal is to remove the tedious and error-prone "update
+the embedded version string" step from your release process. Making a new
+release should be as easy as recording a new tag in your version-control
+system, and maybe making new tarballs.
+
+
+## Quick Install
+
+* `pip install versioneer` to somewhere to your $PATH
+* run `versioneer-installer` in your source tree: this installs `versioneer.py`
+* follow the instructions below (also in the `versioneer.py` docstring)
+
+## Version Identifiers
+
+Source trees come from a variety of places:
+
+* a version-control system checkout (mostly used by developers)
+* a nightly tarball, produced by build automation
+* a snapshot tarball, produced by a web-based VCS browser, like github's
+ "tarball from tag" feature
+* a release tarball, produced by "setup.py sdist", distributed through PyPI
+
+Within each source tree, the version identifier (either a string or a number,
+this tool is format-agnostic) can come from a variety of places:
+
+* ask the VCS tool itself, e.g. "git describe" (for checkouts), which knows
+ about recent "tags" and an absolute revision-id
+* the name of the directory into which the tarball was unpacked
+* an expanded VCS keyword ($Id$, etc)
+* a `_version.py` created by some earlier build step
+
+For released software, the version identifier is closely related to a VCS
+tag. Some projects use tag names that include more than just the version
+string (e.g. "myproject-1.2" instead of just "1.2"), in which case the tool
+needs to strip the tag prefix to extract the version identifier. For
+unreleased software (between tags), the version identifier should provide
+enough information to help developers recreate the same tree, while also
+giving them an idea of roughly how old the tree is (after version 1.2, before
+version 1.3). Many VCS systems can report a description that captures this,
+for example 'git describe --tags --dirty --always' reports things like
+"0.7-1-g574ab98-dirty" to indicate that the checkout is one revision past the
+0.7 tag, has a unique revision id of "574ab98", and is "dirty" (it has
+uncommitted changes.
+
+The version identifier is used for multiple purposes:
+
+* to allow the module to self-identify its version: `myproject.__version__`
+* to choose a name and prefix for a 'setup.py sdist' tarball
+
+## Theory of Operation
+
+Versioneer works by adding a special `_version.py` file into your source
+tree, where your `__init__.py` can import it. This `_version.py` knows how to
+dynamically ask the VCS tool for version information at import time. However,
+when you use "setup.py build" or "setup.py sdist", `_version.py` in the new
+copy is replaced by a small static file that contains just the generated
+version data.
+
+`_version.py` also contains `$Revision$` markers, and the installation
+process marks `_version.py` to have this marker rewritten with a tag name
+during the "git archive" command. As a result, generated tarballs will
+contain enough information to get the proper version.
+
+
+## Installation
+
+First, decide on values for the following configuration variables:
+
+* `VCS`: the version control system you use. Currently accepts "git".
+
+* `versionfile_source`:
+
+ A project-relative pathname into which the generated version strings should
+ be written. This is usually a `_version.py` next to your project's main
+ `__init__.py` file, so it can be imported at runtime. If your project uses
+ `src/myproject/__init__.py`, this should be `src/myproject/_version.py`.
+ This file should be checked in to your VCS as usual: the copy created below
+ by `setup.py versioneer` will include code that parses expanded VCS
+ keywords in generated tarballs. The 'build' and 'sdist' commands will
+ replace it with a copy that has just the calculated version string.
+
+ This must be set even if your project does not have any modules (and will
+ therefore never import `_version.py`), since "setup.py sdist" -based trees
+ still need somewhere to record the pre-calculated version strings. Anywhere
+ in the source tree should do. If there is a `__init__.py` next to your
+ `_version.py`, the `setup.py versioneer` command (described below) will
+ append some `__version__`-setting assignments, if they aren't already
+ present.
+
+* `versionfile_build`:
+
+ Like `versionfile_source`, but relative to the build directory instead of
+ the source directory. These will differ when your setup.py uses
+ 'package_dir='. If you have `package_dir={'myproject': 'src/myproject'}`,
+ then you will probably have `versionfile_build='myproject/_version.py'` and
+ `versionfile_source='src/myproject/_version.py'`.
+
+ If this is set to None, then `setup.py build` will not attempt to rewrite
+ any `_version.py` in the built tree. If your project does not have any
+ libraries (e.g. if it only builds a script), then you should use
+ `versionfile_build = None` and override `distutils.command.build_scripts`
+ to explicitly insert a copy of `versioneer.get_version()` into your
+ generated script.
+
+* `tag_prefix`:
+
+ a string, like 'PROJECTNAME-', which appears at the start of all VCS tags.
+ If your tags look like 'myproject-1.2.0', then you should use
+ tag_prefix='myproject-'. If you use unprefixed tags like '1.2.0', this
+ should be an empty string.
+
+* `parentdir_prefix`:
+
+ a string, frequently the same as tag_prefix, which appears at the start of
+ all unpacked tarball filenames. If your tarball unpacks into
+ 'myproject-1.2.0', this should be 'myproject-'.
+
+This tool provides one script, named `versioneer-installer`. That script does
+one thing: write a copy of `versioneer.py` into the current directory.
+
+To versioneer-enable your project:
+
+* 1: Run `versioneer-installer` to copy `versioneer.py` into the top of your
+ source tree.
+
+* 2: add the following lines to the top of your `setup.py`, with the
+ configuration values you decided earlier:
+
+ import versioneer
+ versioneer.VCS = 'git'
+ versioneer.versionfile_source = 'src/myproject/_version.py'
+ versioneer.versionfile_build = 'myproject/_version.py'
+ versioneer.tag_prefix = '' # tags are like 1.2.0
+ versioneer.parentdir_prefix = 'myproject-' # dirname like 'myproject-1.2.0'
+
+* 3: add the following arguments to the setup() call in your setup.py:
+
+ version=versioneer.get_version(),
+ cmdclass=versioneer.get_cmdclass(),
+
+* 4: now run `setup.py versioneer`, which will create `_version.py`, and will
+ modify your `__init__.py` (if one exists next to `_version.py`) to define
+ `__version__` (by calling a function from `_version.py`). It will also
+ modify your `MANIFEST.in` to include both `versioneer.py` and the generated
+ `_version.py` in sdist tarballs.
+
+* 5: commit these changes to your VCS. To make sure you won't forget,
+ `setup.py versioneer` will mark everything it touched for addition.
+
+## Post-Installation Usage
+
+Once established, all uses of your tree from a VCS checkout should get the
+current version string. All generated tarballs should include an embedded
+version string (so users who unpack them will not need a VCS tool installed).
+
+If you distribute your project through PyPI, then the release process should
+boil down to two steps:
+
+* 1: git tag 1.0
+* 2: python setup.py register sdist upload
+
+If you distribute it through github (i.e. users use github to generate
+tarballs with `git archive`), the process is:
+
+* 1: git tag 1.0
+* 2: git push; git push --tags
+
+Currently, all version strings must be based upon a tag. Versioneer will
+report "unknown" until your tree has at least one tag in its history. This
+restriction will be fixed eventually (see issue #12).
+
+## Version-String Flavors
+
+Code which uses Versioneer can learn about its version string at runtime by
+importing `_version` from your main `__init__.py` file and running the
+`get_versions()` function. From the "outside" (e.g. in `setup.py`), you can
+import the top-level `versioneer.py` and run `get_versions()`.
+
+Both functions return a dictionary with different keys for different flavors
+of the version string:
+
+* `['version']`: condensed tag+distance+shortid+dirty identifier. For git,
+ this uses the output of `git describe --tags --dirty --always` but strips
+ the tag_prefix. For example "0.11-2-g1076c97-dirty" indicates that the tree
+ is like the "1076c97" commit but has uncommitted changes ("-dirty"), and
+ that this commit is two revisions ("-2-") beyond the "0.11" tag. For
+ released software (exactly equal to a known tag), the identifier will only
+ contain the stripped tag, e.g. "0.11".
+
+* `['full']`: detailed revision identifier. For Git, this is the full SHA1
+ commit id, followed by "-dirty" if the tree contains uncommitted changes,
+ e.g. "1076c978a8d3cfc70f408fe5974aa6c092c949ac-dirty".
+
+Some variants are more useful than others. Including `full` in a bug report
+should allow developers to reconstruct the exact code being tested (or
+indicate the presence of local changes that should be shared with the
+developers). `version` is suitable for display in an "about" box or a CLI
+`--version` output: it can be easily compared against release notes and lists
+of bugs fixed in various releases.
+
+In the future, this will also include a
+[PEP-0440](http://legacy.python.org/dev/peps/pep-0440/) -compatible flavor
+(e.g. `1.2.post0.dev123`). This loses a lot of information (and has no room
+for a hash-based revision id), but is safe to use in a `setup.py`
+"`version=`" argument. It also enables tools like *pip* to compare version
+strings and evaluate compatibility constraint declarations.
+
+The `setup.py versioneer` command adds the following text to your
+`__init__.py` to place a basic version in `YOURPROJECT.__version__`:
+
+ from ._version import get_versions
+ __version__ = get_versions()['version']
+ del get_versions
+
+## Updating Versioneer
+
+To upgrade your project to a new release of Versioneer, do the following:
+
+* install the new Versioneer (`pip install -U versioneer` or equivalent)
+* re-run `versioneer-installer` in your source tree to replace your copy of
+ `versioneer.py`
+* edit `setup.py`, if necessary, to include any new configuration settings
+ indicated by the release notes
+* re-run `setup.py versioneer` to replace `SRC/_version.py`
+* commit any changed files
+
+### Upgrading from 0.10 to 0.11
+
+You must add a `versioneer.VCS = "git"` to your `setup.py` before re-running
+`setup.py versioneer`. This will enable the use of additional version-control
+systems (SVN, etc) in the future.
+
+### Upgrading from 0.11 to 0.12
+
+Nothing special.
+
+## Future Directions
+
+This tool is designed to make it easily extended to other version-control
+systems: all VCS-specific components are in separate directories like
+src/git/ . The top-level `versioneer.py` script is assembled from these
+components by running make-versioneer.py . In the future, make-versioneer.py
+will take a VCS name as an argument, and will construct a version of
+`versioneer.py` that is specific to the given VCS. It might also take the
+configuration arguments that are currently provided manually during
+installation by editing setup.py . Alternatively, it might go the other
+direction and include code from all supported VCS systems, reducing the
+number of intermediate scripts.
+
+
+## License
+
+To make Versioneer easier to embed, all its code is hereby released into the
+public domain. The `_version.py` that it creates is also in the public
+domain.
+
+"""
+
+import os, sys, re, subprocess, errno
+from distutils.core import Command
+from distutils.command.sdist import sdist as _sdist
+from distutils.command.build import build as _build
+
+# these configuration settings will be overridden by setup.py after it
+# imports us
+versionfile_source = None
+versionfile_build = None
+tag_prefix = None
+parentdir_prefix = None
+VCS = None
+
+# these dictionaries contain VCS-specific tools
+LONG_VERSION_PY = {}
+
+def run_command(commands, args, cwd=None, verbose=False, hide_stderr=False):
+ assert isinstance(commands, list)
+ p = None
+ for c in commands:
+ try:
+ # remember shell=False, so use git.cmd on windows, not just git
+ p = subprocess.Popen([c] + args, cwd=cwd, stdout=subprocess.PIPE,
+ stderr=(subprocess.PIPE if hide_stderr
+ else None))
+ break
+ except EnvironmentError:
+ e = sys.exc_info()[1]
+ if e.errno == errno.ENOENT:
+ continue
+ if verbose:
+ print("unable to run %s" % args[0])
+ print(e)
+ return None
+ else:
+ if verbose:
+ print("unable to find command, tried %s" % (commands,))
+ return None
+ stdout = p.communicate()[0].strip()
+ if sys.version >= '3':
+ stdout = stdout.decode()
+ if p.returncode != 0:
+ if verbose:
+ print("unable to run %s (error)" % args[0])
+ return None
+ return stdout
+
+LONG_VERSION_PY['git'] = '''
+# This file helps to compute a version number in source trees obtained from
+# git-archive tarball (such as those provided by githubs download-from-tag
+# feature). Distribution tarballs (built by setup.py sdist) and build
+# directories (produced by setup.py build) will contain a much shorter file
+# that just contains the computed version number.
+
+# This file is released into the public domain. Generated by
+# versioneer-0.12 (https://github.com/warner/python-versioneer)
+
+# these strings will be replaced by git during git-archive
+git_refnames = "%(DOLLAR)sFormat:%%d%(DOLLAR)s"
+git_full = "%(DOLLAR)sFormat:%%H%(DOLLAR)s"
+
+# these strings are filled in when 'setup.py versioneer' creates _version.py
+tag_prefix = "%(TAG_PREFIX)s"
+parentdir_prefix = "%(PARENTDIR_PREFIX)s"
+versionfile_source = "%(VERSIONFILE_SOURCE)s"
+
+import os, sys, re, subprocess, errno
+
+def run_command(commands, args, cwd=None, verbose=False, hide_stderr=False):
+ assert isinstance(commands, list)
+ p = None
+ for c in commands:
+ try:
+ # remember shell=False, so use git.cmd on windows, not just git
+ p = subprocess.Popen([c] + args, cwd=cwd, stdout=subprocess.PIPE,
+ stderr=(subprocess.PIPE if hide_stderr
+ else None))
+ break
+ except EnvironmentError:
+ e = sys.exc_info()[1]
+ if e.errno == errno.ENOENT:
+ continue
+ if verbose:
+ print("unable to run %%s" %% args[0])
+ print(e)
+ return None
+ else:
+ if verbose:
+ print("unable to find command, tried %%s" %% (commands,))
+ return None
+ stdout = p.communicate()[0].strip()
+ if sys.version >= '3':
+ stdout = stdout.decode()
+ if p.returncode != 0:
+ if verbose:
+ print("unable to run %%s (error)" %% args[0])
+ return None
+ return stdout
+
+
+def versions_from_parentdir(parentdir_prefix, root, verbose=False):
+ # Source tarballs conventionally unpack into a directory that includes
+ # both the project name and a version string.
+ dirname = os.path.basename(root)
+ if not dirname.startswith(parentdir_prefix):
+ if verbose:
+ print("guessing rootdir is '%%s', but '%%s' doesn't start with prefix '%%s'" %%
+ (root, dirname, parentdir_prefix))
+ return None
+ return {"version": dirname[len(parentdir_prefix):], "full": ""}
+
+def git_get_keywords(versionfile_abs):
+ # the code embedded in _version.py can just fetch the value of these
+ # keywords. When used from setup.py, we don't want to import _version.py,
+ # so we do it with a regexp instead. This function is not used from
+ # _version.py.
+ keywords = {}
+ try:
+ f = open(versionfile_abs,"r")
+ for line in f.readlines():
+ if line.strip().startswith("git_refnames ="):
+ mo = re.search(r'=\s*"(.*)"', line)
+ if mo:
+ keywords["refnames"] = mo.group(1)
+ if line.strip().startswith("git_full ="):
+ mo = re.search(r'=\s*"(.*)"', line)
+ if mo:
+ keywords["full"] = mo.group(1)
+ f.close()
+ except EnvironmentError:
+ pass
+ return keywords
+
+def git_versions_from_keywords(keywords, tag_prefix, verbose=False):
+ if not keywords:
+ return {} # keyword-finding function failed to find keywords
+ refnames = keywords["refnames"].strip()
+ if refnames.startswith("$Format"):
+ if verbose:
+ print("keywords are unexpanded, not using")
+ return {} # unexpanded, so not in an unpacked git-archive tarball
+ refs = set([r.strip() for r in refnames.strip("()").split(",")])
+ # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of
+ # just "foo-1.0". If we see a "tag: " prefix, prefer those.
+ TAG = "tag: "
+ tags = set([r[len(TAG):] for r in refs if r.startswith(TAG)])
+ if not tags:
+ # Either we're using git < 1.8.3, or there really are no tags. We use
+ # a heuristic: assume all version tags have a digit. The old git %%d
+ # expansion behaves like git log --decorate=short and strips out the
+ # refs/heads/ and refs/tags/ prefixes that would let us distinguish
+ # between branches and tags. By ignoring refnames without digits, we
+ # filter out many common branch names like "release" and
+ # "stabilization", as well as "HEAD" and "master".
+ tags = set([r for r in refs if re.search(r'\d', r)])
+ if verbose:
+ print("discarding '%%s', no digits" %% ",".join(refs-tags))
+ if verbose:
+ print("likely tags: %%s" %% ",".join(sorted(tags)))
+ for ref in sorted(tags):
+ # sorting will prefer e.g. "2.0" over "2.0rc1"
+ if ref.startswith(tag_prefix):
+ r = ref[len(tag_prefix):]
+ if verbose:
+ print("picking %%s" %% r)
+ return { "version": r,
+ "full": keywords["full"].strip() }
+ # no suitable tags, so we use the full revision id
+ if verbose:
+ print("no suitable tags, using full revision id")
+ return { "version": keywords["full"].strip(),
+ "full": keywords["full"].strip() }
+
+
+def git_versions_from_vcs(tag_prefix, root, verbose=False):
+ # this runs 'git' from the root of the source tree. This only gets called
+ # if the git-archive 'subst' keywords were *not* expanded, and
+ # _version.py hasn't already been rewritten with a short version string,
+ # meaning we're inside a checked out source tree.
+
+ if not os.path.exists(os.path.join(root, ".git")):
+ if verbose:
+ print("no .git in %%s" %% root)
+ return {}
+
+ GITS = ["git"]
+ if sys.platform == "win32":
+ GITS = ["git.cmd", "git.exe"]
+ stdout = run_command(GITS, ["describe", "--tags", "--dirty", "--always"],
+ cwd=root)
+ if stdout is None:
+ return {}
+ if not stdout.startswith(tag_prefix):
+ if verbose:
+ print("tag '%%s' doesn't start with prefix '%%s'" %% (stdout, tag_prefix))
+ return {}
+ tag = stdout[len(tag_prefix):]
+ stdout = run_command(GITS, ["rev-parse", "HEAD"], cwd=root)
+ if stdout is None:
+ return {}
+ full = stdout.strip()
+ if tag.endswith("-dirty"):
+ full += "-dirty"
+ return {"version": tag, "full": full}
+
+
+def get_versions(default={"version": "unknown", "full": ""}, verbose=False):
+ # I am in _version.py, which lives at ROOT/VERSIONFILE_SOURCE. If we have
+ # __file__, we can work backwards from there to the root. Some
+ # py2exe/bbfreeze/non-CPython implementations don't do __file__, in which
+ # case we can only use expanded keywords.
+
+ keywords = { "refnames": git_refnames, "full": git_full }
+ ver = git_versions_from_keywords(keywords, tag_prefix, verbose)
+ if ver:
+ return ver
+
+ try:
+ root = os.path.abspath(__file__)
+ # versionfile_source is the relative path from the top of the source
+ # tree (where the .git directory might live) to this file. Invert
+ # this to find the root from __file__.
+ for i in range(len(versionfile_source.split(os.sep))):
+ root = os.path.dirname(root)
+ except NameError:
+ return default
+
+ return (git_versions_from_vcs(tag_prefix, root, verbose)
+ or versions_from_parentdir(parentdir_prefix, root, verbose)
+ or default)
+'''
+
+def git_get_keywords(versionfile_abs):
+ # the code embedded in _version.py can just fetch the value of these
+ # keywords. When used from setup.py, we don't want to import _version.py,
+ # so we do it with a regexp instead. This function is not used from
+ # _version.py.
+ keywords = {}
+ try:
+ f = open(versionfile_abs,"r")
+ for line in f.readlines():
+ if line.strip().startswith("git_refnames ="):
+ mo = re.search(r'=\s*"(.*)"', line)
+ if mo:
+ keywords["refnames"] = mo.group(1)
+ if line.strip().startswith("git_full ="):
+ mo = re.search(r'=\s*"(.*)"', line)
+ if mo:
+ keywords["full"] = mo.group(1)
+ f.close()
+ except EnvironmentError:
+ pass
+ return keywords
+
+def git_versions_from_keywords(keywords, tag_prefix, verbose=False):
+ if not keywords:
+ return {} # keyword-finding function failed to find keywords
+ refnames = keywords["refnames"].strip()
+ if refnames.startswith("$Format"):
+ if verbose:
+ print("keywords are unexpanded, not using")
+ return {} # unexpanded, so not in an unpacked git-archive tarball
+ refs = set([r.strip() for r in refnames.strip("()").split(",")])
+ # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of
+ # just "foo-1.0". If we see a "tag: " prefix, prefer those.
+ TAG = "tag: "
+ tags = set([r[len(TAG):] for r in refs if r.startswith(TAG)])
+ if not tags:
+ # Either we're using git < 1.8.3, or there really are no tags. We use
+ # a heuristic: assume all version tags have a digit. The old git %d
+ # expansion behaves like git log --decorate=short and strips out the
+ # refs/heads/ and refs/tags/ prefixes that would let us distinguish
+ # between branches and tags. By ignoring refnames without digits, we
+ # filter out many common branch names like "release" and
+ # "stabilization", as well as "HEAD" and "master".
+ tags = set([r for r in refs if re.search(r'\d', r)])
+ if verbose:
+ print("discarding '%s', no digits" % ",".join(refs-tags))
+ if verbose:
+ print("likely tags: %s" % ",".join(sorted(tags)))
+ for ref in sorted(tags):
+ # sorting will prefer e.g. "2.0" over "2.0rc1"
+ if ref.startswith(tag_prefix):
+ r = ref[len(tag_prefix):]
+ if verbose:
+ print("picking %s" % r)
+ return { "version": r,
+ "full": keywords["full"].strip() }
+ # no suitable tags, so we use the full revision id
+ if verbose:
+ print("no suitable tags, using full revision id")
+ return { "version": keywords["full"].strip(),
+ "full": keywords["full"].strip() }
+
+
+def git_versions_from_vcs(tag_prefix, root, verbose=False):
+ # this runs 'git' from the root of the source tree. This only gets called
+ # if the git-archive 'subst' keywords were *not* expanded, and
+ # _version.py hasn't already been rewritten with a short version string,
+ # meaning we're inside a checked out source tree.
+
+ if not os.path.exists(os.path.join(root, ".git")):
+ if verbose:
+ print("no .git in %s" % root)
+ return {}
+
+ GITS = ["git"]
+ if sys.platform == "win32":
+ GITS = ["git.cmd", "git.exe"]
+ stdout = run_command(GITS, ["describe", "--tags", "--dirty", "--always"],
+ cwd=root)
+ if stdout is None:
+ return {}
+ if not stdout.startswith(tag_prefix):
+ if verbose:
+ print("tag '%s' doesn't start with prefix '%s'" % (stdout, tag_prefix))
+ return {}
+ tag = stdout[len(tag_prefix):]
+ stdout = run_command(GITS, ["rev-parse", "HEAD"], cwd=root)
+ if stdout is None:
+ return {}
+ full = stdout.strip()
+ if tag.endswith("-dirty"):
+ full += "-dirty"
+ return {"version": tag, "full": full}
+
+
+def do_vcs_install(manifest_in, versionfile_source, ipy):
+ GITS = ["git"]
+ if sys.platform == "win32":
+ GITS = ["git.cmd", "git.exe"]
+ files = [manifest_in, versionfile_source]
+ if ipy:
+ files.append(ipy)
+ try:
+ me = __file__
+ if me.endswith(".pyc") or me.endswith(".pyo"):
+ me = os.path.splitext(me)[0] + ".py"
+ versioneer_file = os.path.relpath(me)
+ except NameError:
+ versioneer_file = "versioneer.py"
+ files.append(versioneer_file)
+ present = False
+ try:
+ f = open(".gitattributes", "r")
+ for line in f.readlines():
+ if line.strip().startswith(versionfile_source):
+ if "export-subst" in line.strip().split()[1:]:
+ present = True
+ f.close()
+ except EnvironmentError:
+ pass
+ if not present:
+ f = open(".gitattributes", "a+")
+ f.write("%s export-subst\n" % versionfile_source)
+ f.close()
+ files.append(".gitattributes")
+ run_command(GITS, ["add", "--"] + files)
+
+def versions_from_parentdir(parentdir_prefix, root, verbose=False):
+ # Source tarballs conventionally unpack into a directory that includes
+ # both the project name and a version string.
+ dirname = os.path.basename(root)
+ if not dirname.startswith(parentdir_prefix):
+ if verbose:
+ print("guessing rootdir is '%s', but '%s' doesn't start with prefix '%s'" %
+ (root, dirname, parentdir_prefix))
+ return None
+ return {"version": dirname[len(parentdir_prefix):], "full": ""}
+
+SHORT_VERSION_PY = """
+# This file was generated by 'versioneer.py' (0.12) from
+# revision-control system data, or from the parent directory name of an
+# unpacked source archive. Distribution tarballs contain a pre-generated copy
+# of this file.
+
+version_version = '%(version)s'
+version_full = '%(full)s'
+def get_versions(default={}, verbose=False):
+ return {'version': version_version, 'full': version_full}
+
+"""
+
+DEFAULT = {"version": "unknown", "full": "unknown"}
+
+def versions_from_file(filename):
+ versions = {}
+ try:
+ with open(filename) as f:
+ for line in f.readlines():
+ mo = re.match("version_version = '([^']+)'", line)
+ if mo:
+ versions["version"] = mo.group(1)
+ mo = re.match("version_full = '([^']+)'", line)
+ if mo:
+ versions["full"] = mo.group(1)
+ except EnvironmentError:
+ return {}
+
+ return versions
+
+def write_to_version_file(filename, versions):
+ with open(filename, "w") as f:
+ f.write(SHORT_VERSION_PY % versions)
+
+ print("set %s to '%s'" % (filename, versions["version"]))
+
+
+def get_root():
+ try:
+ return os.path.dirname(os.path.abspath(__file__))
+ except NameError:
+ return os.path.dirname(os.path.abspath(sys.argv[0]))
+
+def vcs_function(vcs, suffix):
+ return getattr(sys.modules[__name__], '%s_%s' % (vcs, suffix), None)
+
+def get_versions(default=DEFAULT, verbose=False):
+ # returns dict with two keys: 'version' and 'full'
+ assert versionfile_source is not None, "please set versioneer.versionfile_source"
+ assert tag_prefix is not None, "please set versioneer.tag_prefix"
+ assert parentdir_prefix is not None, "please set versioneer.parentdir_prefix"
+ assert VCS is not None, "please set versioneer.VCS"
+
+ # I am in versioneer.py, which must live at the top of the source tree,
+ # which we use to compute the root directory. py2exe/bbfreeze/non-CPython
+ # don't have __file__, in which case we fall back to sys.argv[0] (which
+ # ought to be the setup.py script). We prefer __file__ since that's more
+ # robust in cases where setup.py was invoked in some weird way (e.g. pip)
+ root = get_root()
+ versionfile_abs = os.path.join(root, versionfile_source)
+
+ # extract version from first of _version.py, VCS command (e.g. 'git
+ # describe'), parentdir. This is meant to work for developers using a
+ # source checkout, for users of a tarball created by 'setup.py sdist',
+ # and for users of a tarball/zipball created by 'git archive' or github's
+ # download-from-tag feature or the equivalent in other VCSes.
+
+ get_keywords_f = vcs_function(VCS, "get_keywords")
+ versions_from_keywords_f = vcs_function(VCS, "versions_from_keywords")
+ if get_keywords_f and versions_from_keywords_f:
+ vcs_keywords = get_keywords_f(versionfile_abs)
+ ver = versions_from_keywords_f(vcs_keywords, tag_prefix)
+ if ver:
+ if verbose: print("got version from expanded keyword %s" % ver)
+ return ver
+
+ ver = versions_from_file(versionfile_abs)
+ if ver:
+ if verbose: print("got version from file %s %s" % (versionfile_abs,ver))
+ return ver
+
+ versions_from_vcs_f = vcs_function(VCS, "versions_from_vcs")
+ if versions_from_vcs_f:
+ ver = versions_from_vcs_f(tag_prefix, root, verbose)
+ if ver:
+ if verbose: print("got version from VCS %s" % ver)
+ return ver
+
+ ver = versions_from_parentdir(parentdir_prefix, root, verbose)
+ if ver:
+ if verbose: print("got version from parentdir %s" % ver)
+ return ver
+
+ if verbose: print("got version from default %s" % default)
+ return default
+
+def get_version(verbose=False):
+ return get_versions(verbose=verbose)["version"]
+
+class cmd_version(Command):
+ description = "report generated version string"
+ user_options = []
+ boolean_options = []
+ def initialize_options(self):
+ pass
+ def finalize_options(self):
+ pass
+ def run(self):
+ ver = get_version(verbose=True)
+ print("Version is currently: %s" % ver)
+
+
+class cmd_build(_build):
+ def run(self):
+ versions = get_versions(verbose=True)
+ _build.run(self)
+ # now locate _version.py in the new build/ directory and replace it
+ # with an updated value
+ if versionfile_build:
+ target_versionfile = os.path.join(self.build_lib, versionfile_build)
+ print("UPDATING %s" % target_versionfile)
+ os.unlink(target_versionfile)
+ with open(target_versionfile, "w") as f:
+ f.write(SHORT_VERSION_PY % versions)
+
+if 'cx_Freeze' in sys.modules: # cx_freeze enabled?
+ from cx_Freeze.dist import build_exe as _build_exe
+
+ class cmd_build_exe(_build_exe):
+ def run(self):
+ versions = get_versions(verbose=True)
+ target_versionfile = versionfile_source
+ print("UPDATING %s" % target_versionfile)
+ os.unlink(target_versionfile)
+ with open(target_versionfile, "w") as f:
+ f.write(SHORT_VERSION_PY % versions)
+
+ _build_exe.run(self)
+ os.unlink(target_versionfile)
+ with open(versionfile_source, "w") as f:
+ assert VCS is not None, "please set versioneer.VCS"
+ LONG = LONG_VERSION_PY[VCS]
+ f.write(LONG % {"DOLLAR": "$",
+ "TAG_PREFIX": tag_prefix,
+ "PARENTDIR_PREFIX": parentdir_prefix,
+ "VERSIONFILE_SOURCE": versionfile_source,
+ })
+
+class cmd_sdist(_sdist):
+ def run(self):
+ versions = get_versions(verbose=True)
+ self._versioneer_generated_versions = versions
+ # unless we update this, the command will keep using the old version
+ self.distribution.metadata.version = versions["version"]
+ return _sdist.run(self)
+
+ def make_release_tree(self, base_dir, files):
+ _sdist.make_release_tree(self, base_dir, files)
+ # now locate _version.py in the new base_dir directory (remembering
+ # that it may be a hardlink) and replace it with an updated value
+ target_versionfile = os.path.join(base_dir, versionfile_source)
+ print("UPDATING %s" % target_versionfile)
+ os.unlink(target_versionfile)
+ with open(target_versionfile, "w") as f:
+ f.write(SHORT_VERSION_PY % self._versioneer_generated_versions)
+
+INIT_PY_SNIPPET = """
+from ._version import get_versions
+__version__ = get_versions()['version']
+del get_versions
+"""
+
+class cmd_update_files(Command):
+ description = "install/upgrade Versioneer files: __init__.py SRC/_version.py"
+ user_options = []
+ boolean_options = []
+ def initialize_options(self):
+ pass
+ def finalize_options(self):
+ pass
+ def run(self):
+ print(" creating %s" % versionfile_source)
+ with open(versionfile_source, "w") as f:
+ assert VCS is not None, "please set versioneer.VCS"
+ LONG = LONG_VERSION_PY[VCS]
+ f.write(LONG % {"DOLLAR": "$",
+ "TAG_PREFIX": tag_prefix,
+ "PARENTDIR_PREFIX": parentdir_prefix,
+ "VERSIONFILE_SOURCE": versionfile_source,
+ })
+
+ ipy = os.path.join(os.path.dirname(versionfile_source), "__init__.py")
+ if os.path.exists(ipy):
+ try:
+ with open(ipy, "r") as f:
+ old = f.read()
+ except EnvironmentError:
+ old = ""
+ if INIT_PY_SNIPPET not in old:
+ print(" appending to %s" % ipy)
+ with open(ipy, "a") as f:
+ f.write(INIT_PY_SNIPPET)
+ else:
+ print(" %s unmodified" % ipy)
+ else:
+ print(" %s doesn't exist, ok" % ipy)
+ ipy = None
+
+ # Make sure both the top-level "versioneer.py" and versionfile_source
+ # (PKG/_version.py, used by runtime code) are in MANIFEST.in, so
+ # they'll be copied into source distributions. Pip won't be able to
+ # install the package without this.
+ manifest_in = os.path.join(get_root(), "MANIFEST.in")
+ simple_includes = set()
+ try:
+ with open(manifest_in, "r") as f:
+ for line in f:
+ if line.startswith("include "):
+ for include in line.split()[1:]:
+ simple_includes.add(include)
+ except EnvironmentError:
+ pass
+ # That doesn't cover everything MANIFEST.in can do
+ # (http://docs.python.org/2/distutils/sourcedist.html#commands), so
+ # it might give some false negatives. Appending redundant 'include'
+ # lines is safe, though.
+ if "versioneer.py" not in simple_includes:
+ print(" appending 'versioneer.py' to MANIFEST.in")
+ with open(manifest_in, "a") as f:
+ f.write("include versioneer.py\n")
+ else:
+ print(" 'versioneer.py' already in MANIFEST.in")
+ if versionfile_source not in simple_includes:
+ print(" appending versionfile_source ('%s') to MANIFEST.in" %
+ versionfile_source)
+ with open(manifest_in, "a") as f:
+ f.write("include %s\n" % versionfile_source)
+ else:
+ print(" versionfile_source already in MANIFEST.in")
+
+ # Make VCS-specific changes. For git, this means creating/changing
+ # .gitattributes to mark _version.py for export-time keyword
+ # substitution.
+ do_vcs_install(manifest_in, versionfile_source, ipy)
+
+def get_cmdclass():
+ cmds = {'version': cmd_version,
+ 'versioneer': cmd_update_files,
+ 'build': cmd_build,
+ 'sdist': cmd_sdist,
+ }
+ if 'cx_Freeze' in sys.modules: # cx_freeze enabled?
+ cmds['build_exe'] = cmd_build_exe
+ del cmds['build']
+
+ return cmds
--
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